THIRD AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT

Exhibit 10.4

THIRD AMENDMENT TO

THIRD AMENDED AND RESTATED CREDIT AGREEMENT

THIS THIRD AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT (this “Amendment”) is dated as of March 4, 2011 but effective on the Effective Date (as defined below), by and among Century Exploration New Orleans, Inc., a Delaware corporation, Century Exploration Houston, Inc., a Delaware corporation (each herein called a “Borrower,” and collectively, the “Borrowers”), Union Bank, N.A., individually and as administrative agent (“Administrative Agent”), and the Lenders party to the Original Agreement defined below (“Lenders”).

W I T N E S S E T H:

WHEREAS, Borrowers, Administrative Agent and Lenders entered into that certain Third Amended and Restated Credit Agreement dated as of September 4, 2009 (as heretofore amended or modified, the “Original Agreement”), for the purpose and consideration therein expressed, whereby Lenders became obligated to make loans to Borrowers as therein provided; and

WHEREAS, Borrowers, Administrative Agent and Lenders desire to amend the Original Agreement as set forth herein;

NOW, THEREFORE, in consideration of the premises and the mutual covenants and agreements contained herein and in the Original Agreement, in consideration of the loans which may hereafter be made by Lenders to Borrowers, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto do hereby agree as follows:

ARTICLE I.

DEFINITIONS AND REFERENCES

Section 1.1. Terms Defined in the Original Agreement. Unless the context otherwise requires or unless otherwise expressly defined herein, the terms defined in the Original Agreement shall have the same meanings whenever used in this Amendment.

Section 1.2. Other Defined Terms. Unless the context otherwise requires, the following terms when used in this Amendment shall have the meanings assigned to them in this Section 1.2.

“Amendment” means this Third Amendment to Third Amended and Restated Credit Agreement.

“Credit Agreement” means the Original Agreement as amended hereby.

[THIRD AMENDMENT TO

THIRD AMENDED AND RESTATED CREDIT AGREEMENT]

ARTICLE II.

AMENDMENTS TO ORIGINAL AGREEMENT AND LIMITED WAIVER

Section 2.1. Definitions.

(a) Section 1.1 of the Original Agreement is hereby amended to add the following definitions in the correct alphabetical order:

“Concorde” means Concorde Energy, LLC, a Delaware limited liability company.

(b) The definition of “Permitted Distributions” in Section 1.1 of the Original Agreement is hereby restated in its entirety to read as follows:

““Permitted Distributions” means Distributions by Restricted Persons (i) that consist solely of cash dividends and distributions by a Restricted Person in respect of its capital stock or any partnership or other interest in it paid to a Borrower or any other Restricted Person or (ii) that do not exceed $1,750,000 in the aggregate during any Fiscal Quarter, provided, in each case, that at the time of such Distribution and after giving effect thereto, no Event of Default has occurred and is continuing.”

(c) The definitions of “Consolidated” and “Subsidiary” in Section 1.1 of the Original Agreement are hereby restated in their entirety to read as follows:

““Consolidated” refers to the consolidation of any Person, in accordance with GAAP, with its properly consolidated subsidiaries. References herein to a Person’s Consolidated financial statements, financial position, financial condition, liabilities, etc. refer to the consolidated financial statements, financial position, financial condition, liabilities, etc. of such Person and its properly consolidated subsidiaries; provided, however, that, for purposes of the Loan Documents, in no event shall Concorde or any Subsidiary of Concorde be deemed to be a “consolidated subsidiary” of any Restricted Person.”

““Subsidiary” means, with respect to any Person, any corporation, association, partnership, limited liability company, joint venture, or other business or corporate entity, enterprise or organization which is directly or indirectly (through one or more intermediaries) controlled by or owned fifty percent or more by such Person; provided that (i) associations, joint ventures or other relationships (a) which are established pursuant to a standard form operating agreement or similar agreement or which are partnerships for purposes of federal income taxation only, (b) which are not corporations or partnerships (or subject to the Uniform Partnership Act) under applicable state Law, and (c) whose businesses are limited to the exploration, development and operation of oil, gas or mineral properties and interests owned directly by the parties in such associations,

joint ventures or relationships, shall not be deemed to be “Subsidiaries” of such Person and (ii) in no event shall Concorde or its Subsidiaries be deemed to be a Subsidiary of any Restricted Person for any purpose under the Loan Documents.”

Section 2.2. Calculations and Determinations. The final sentence of Section 1.4 of the Original Credit Agreement is hereby amended to add the following proviso to the end thereof:

“; provided, however, that for purposes of calculating the ratios in Sections 7.13 and 7.14 and the components of each such ratio, Concorde and its Subsidiaries (including their respective assets, liabilities, income, losses, cash flows, interest expense and each element of the foregoing) shall be excluded, except for any cash dividends or distributions actually paid by Concorde or its Subsidiaries to any Restricted Person, which shall be deemed to be income of the applicable Restricted Person when actually received by it.”

Section 2.3. Representations and Warranties. Section 5.22, Section 5.23 and the last sentence of Section 5.24 are hereby amended by adding the phrase “of the Restricted Persons” immediately following each occurrence of the phrase “Oil and Gas Property” or “Oil and Gas Properties”, respectively.

Section 2.4. Books, Financial Statements and Reports. Sections 6.2(a) and (b) or the Original Agreement are hereby restated in their entirety to read as follows:

“(a) As soon as available, and in any event within one hundred twenty (120) days after the end of each Fiscal Year, complete Consolidated and consolidating financial statements of RAAM together with all notes thereto, prepared in reasonable detail in accordance with GAAP, together with an unqualified opinion, based on an audit using generally accepted auditing standards, by a “Big Four” public accounting firm or another independent certified public accounting firm selected by RAAM and acceptable to Lender, stating that such Consolidated financial statements have been so prepared. These financial statements shall contain (i) a Consolidated and consolidating balance sheet as of the end of such Fiscal Year and Consolidated and consolidating statements of earnings, of cash flows, and of changes in owners’ equity for such Fiscal Year, each setting forth in comparative form the corresponding figures for the preceding Fiscal Year and (ii) during any period during which GAAP would otherwise require Concorde’s and its Subsidiaries’ accounts to be consolidated with those of RAAM, consolidating financial statements, prepared in a manner consistent with RAAM’s historical practices, distinguishing the consolidated accounts of the Restricted Persons from the consolidated accounts of Concorde and its Subsidiaries, provided that the consolidating financial statements referred to in clause (ii) of this Section 6.2(a) shall not be required to be audited or covered by the opinion of the auditors referred to above.

“(b) As soon as available, and in any event within sixty (60) days after the end of each Fiscal Quarter, a balance sheet as of the end of such Fiscal Quarter and Consolidated and consolidating statements of RAAM’s earnings and cash flows for the period from the beginning of the then current Fiscal Year to the end of such Fiscal Quarter, all in reasonable detail and prepared in accordance with GAAP, subject to changes resulting from normal year-end adjustments and, during any period during which GAAP would otherwise require Concorde’s and its Subsidiaries’ accounts to be consolidated with those of RAAM, a consolidating balance sheet and consolidating financial statements, prepared in a manner consistent with RAAM’s historical practices, distinguishing the consolidated accounts of the Restricted Persons from the consolidated accounts of Concorde and its Subsidiaries. In addition, RAAM will, together with each such set of financial statements and each set of financial statements furnished under subsection (a) of this section, furnish a certificate in the form of Exhibit D stating that the chief financial officer has reviewed the Loan Documents, containing calculations showing compliance (or non-compliance) at the end of such Fiscal Quarter with the requirements of Sections 7.3, 7.4, 7.13, 7.14 and 7.15 and stating that no Default exists at the end of such Fiscal Quarter or at the time of such certificate or specifying the nature and period of existence of any such Default.”

Section 2.5. Hedging Contracts. The reference to “twenty-four (24) months” in the first sentence of Section 7.4 of the Original Agreement is hereby amended to read “thirty-six (36) months.”

Section 2.6. Limitation on Investments and New Businesses. Subsection (iii) of Section 7.8 of the Original Agreement is hereby amended in its entirety to read as follows:

“(iii) make any acquisitions of or capital contributions to or other Investments in any Person that is not a Restricted Person, other than (x) Cash Equivalents or (y) Investments by RAAM in Concorde in an aggregate amount not to exceed $35,000,000, and”

Section 2.7. Transactions with Affiliates. Section 7.10 of the Original Agreement is hereby restated in its entirety to read as follows:

“Section 7.10 Transactions with Affiliates. Other than Investments by RAAM in Concorde permitted by Section 7.8 (iii) and agreements among Concorde and any Restricted Person for the provision of management services and general and administrative services, no Restricted Person will engage in any material transaction with any of its Affiliates on terms which are less favorable to it than those which would have been obtainable at the time in arm’s-length dealing with Persons other than such Affiliates.”

Section 2.8. Disclosure Schedule – Disclosure Schedule 5.14 – Borrowers’ Subsidiaries. Disclosure Schedule 5.14 of the Original Agreement is hereby restated in its entirety to read as set forth on Disclosure Schedule 5.14 attached hereto.

Section 2.9. Limited Waiver. CEH has informed Administrative Agent that on or about January 28, 2011, CEH disposed of certain Oil and Gas Properties in the Tuscaloosa Marine oil shale prospect (the “Tuscaloosa Marine Properties”) to Devon Energy Production Company, L.P. for a purchase price of $13,836,462.25 (the “Tuscaloosa Marine Disposition”). The Tuscaloosa Marine Disposition was a disposition of Oil and Gas Properties for fair market value and the Tuscaloosa Marine Properties did not constitute Collateral as the time of the sale. The value of the Tuscaloosa Marine Properties (as evidenced by the purchase price), however, was in excess of 10% of the Borrowing Base in effect at the time of the Tuscaloosa Marine Disposition, and the Tuscaloosa Marine Disposition was therefore prohibited by Section 7.6 of the Credit Agreement. The Restricted Persons have requested that Majority Lenders waive this violation of Section 7.6 of the Credit Agreement (and any related Event of Default) arising from the Tuscaloosa Marine Disposition. Subject to the terms, conditions and limitations of this Amendment, Majority Lenders hereby waive any violation of Section 7.6 of the Credit Agreement (and any related Event of Default) arising from the Tuscaloosa Marine Disposition.

Section 2.10. Release of Liens. Pursuant to that certain Limited Waiver and Consent dated as of September 23, 2010 among Borrowers, the other Restricted Persons, Administrative Agent and Majority Lenders (the “Limited Waiver”), Majority Lenders waived certain violations of the Credit Agreement arising from the existence of Indebtedness in respect of the GE Note (as defined in the Limited Waiver) and Liens pursuant to the GE Mortgage (as defined in the Limited Waiver), including, without limitation, Liens in the GE Mortgage Personal Property (as defined in the Limited Waiver and described as the “Property” in the GE Mortgage). Pursuant to the Security Documents, RAAM has granted Liens in the GE Personal Property in favor of Administrative Agent to secure the Secured Obligations and, as such, the GE Personal Property currently constitutes Collateral. RAAM has requested that Majority Lenders (i) release all Liens in the in the “Property”, as defined in the GE Mortgage (the “Released Property”) and (ii) authorize Administrative Agent to take any action necessary to release all Liens granted by the Security Documents in the Released Property. Subject to the terms, conditions and limitations of this Amendment, Majority Lenders hereby consent to the release of all Liens in the Released Property and authorize Administrative Agent to take any action necessary to release the Liens granted by the Security Documents in the Released Property.

ARTICLE III.

CONDITIONS OF EFFECTIVENESS

Section 3.1. Effective Date. This Amendment shall be effective on the date (the “Effective Date”) the Administrative Agent shall have received, at Administrative Agent’s office, (i) this Amendment executed and delivered by each Borrower and Majority Lenders and (ii) a Consent and Agreement of even date herewith executed by RAAM and each other Guarantor.

ARTICLE IV.

REPRESENTATIONS AND WARRANTIES

Section 4.1. Representations and Warranties of Borrowers. In order to induce each Lender to enter into this Amendment, each Borrower jointly and severally represents and warrants to each Lender that:

(a) The representations and warranties contained in Article V of the Original Agreement are true and correct at and as of the time of the effectiveness hereof, except to the extent that the facts on which such representations and warranties are based have been changed by the extension of credit under the Credit Agreement.

(b) Such Borrower is duly authorized to execute and deliver this Amendment and is and will continue to be duly authorized to borrow monies and to perform its obligations under the Credit Agreement. Such Borrower has duly taken all corporate action necessary to authorize the execution and delivery of this Amendment and to authorize the performance of the obligations of such Borrower hereunder.

(c) The execution and delivery by such Borrower of this Amendment, the performance by such Borrower of its obligations hereunder and the consummation of the transactions contemplated hereby do not and will not (i) conflict with any provision of (1) any Law, (2) the organizational documents of such Borrower, or (3) any material agreement, judgment, license, order or permit applicable to or binding upon such Borrower, or (ii) result in the creation of any Lien upon any assets or properties of such Borrower except as expressly contemplated or permitted in the Loan Documents. Except as expressly contemplated in the Loan Documents, no consent, approval, authorization or order of any Tribunal or third party is required in connection with the execution and delivery by such Borrower of this Amendment or to consummate the transactions contemplated hereby.

(d) When duly executed and delivered, each of this Amendment and the Credit Agreement will be a legal and binding obligation of such Borrower, enforceable in accordance with its terms, except as limited by bankruptcy, insolvency or similar Laws of general application relating to the enforcement of creditors’ rights and by equitable principles of general application.

ARTICLE V.

MISCELLANEOUS

Section 5.1. Ratification of Agreements. The Original Agreement as hereby amended is hereby ratified and confirmed in all respects. Any reference to the Credit Agreement in any Loan Document shall be deemed to be a reference to the Original Agreement as hereby amended. The execution, delivery and effectiveness of this Amendment shall not, except as expressly provided herein, operate as a waiver of any right, power or remedy of Lenders under the Credit Agreement, the Notes, or any other Loan Document nor constitute a waiver of any provision of the Credit Agreement, the Notes, or any other Loan Document. Without limitation of the

foregoing, the consents, waivers and agreements set forth herein are limited precisely to the extent set forth herein and shall not be deemed to (a) be a consent or agreement to, or waiver or modification of, any other term or condition of the Credit Agreement or any of the documents referred to therein, or (b) except as expressly set forth herein, prejudice any right or rights that Administrative Agent or Lenders may now have or may have in the future under or in connection with the Credit Agreement or any of the documents referred to therein

Section 5.2. Survival of Agreements. All representations, warranties, covenants and agreements of Borrowers herein shall survive the execution and delivery of this Amendment and the performance hereof, including without limitation the making or granting of the Loans, and shall further survive until all of the Obligations are paid in full. All statements and agreements contained in any certificate or instrument delivered by any Restricted Person hereunder or under the Credit Agreement to any Lender shall be deemed to constitute representations and warranties by, and/or agreements and covenants of, such Restricted Person under this Amendment and under the Credit Agreement.

Section 5.3. Loan Documents. This Amendment is a Loan Document, and all provisions in the Credit Agreement pertaining to Loan Documents apply hereto.

Section 5.4. Governing Law. This Amendment shall be governed in accordance with the Governing Law provisions set forth in Section 10.7 of the Credit Agreement.

Section 5.5. Counterparts; Fax. This Amendment may be separately executed in counterparts and by the different parties hereto in separate counterparts, each of which when so executed shall be deemed to constitute one and the same Amendment. This Amendment may be validly executed by facsimile or other electronic transmission.

THIS AMENDMENT AND THE OTHER LOAN DOCUMENTS REPRESENT THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS OF THE PARTIES.

[The remainder of this past is left blank intentionally.]

IN WITNESS WHEREOF, this Amendment is executed as of the date first above written.

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[THIRD AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT - SIGNATURE PAGE]

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[THIRD AMENDMENT]

CONSENT AND AGREEMENT

The undersigned hereby (i) consents to the provisions of this Amendment and the transactions contemplated herein, (ii) ratifies and confirms the Second Amended and Restated Guaranty dated as of September 4, 2009 (the “Guaranty”) made by it for the benefit of Administrative Agent and Lenders, which Guaranty was executed pursuant to the Credit Agreement and the other Loan Documents, (iii) agrees that all of its respective obligations and covenants under the Guaranty shall remain unimpaired by the execution and delivery of this Amendment and the other documents and instruments executed in connection herewith, and (iv) agrees that the Guaranty and such other Loan Documents shall remain in full force and effect.

[THIRD AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT - CONSENT AND AGREEMENT]

[THIRD AMENDMENT]

CONSENT AND AGREEMENT

Each of the undersigned hereby (i) consents to the provisions of this Amendment and the transactions contemplated herein, (ii) ratifies and confirms the First Amended and Restated Guaranty dated as of September 4, 2009 (the “Guaranty”) made by it for the benefit of Administrative Agent and Lenders, which Guaranty was executed pursuant to the Credit Agreement and the other Loan Documents, (iii) agrees that all of its respective obligations and covenants under the Guaranty shall remain unimpaired by the execution and delivery of this Amendment and the other documents and instruments executed in connection herewith, and (iv) agrees that the Guaranty and such other Loan Documents shall remain in full force and effect.

[THIRD AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT - CONSENT AND AGREEMENT]

BUSINESS SUBSIDIARIES

DISCLOSURE SCHEDULE 5.14

TO THE

THIRD AMENDED AND RESTATED CREDIT AGREEMENT

AMONG

CENTURY EXPLORATION NEW ORLEANS, INC.

CENTURY EXPLORATION HOUSTON, INC.

(as “Borrowers”)

AND

UNION BANK, N.A.

(as “Administrative Agent”)

1. RAAM may acquire a membership interest in Concorde up to the percentage interest it will earn with the investment permitted pursuant to Section 7.8(iii) of the Credit Agreement, which is currently expected to be 25%.

[THIRD AMENDMENT TO THIRD AMENDED AND RESTATED CREDIT AGREEMENT

– DISCLOSURE SCHEDULE 5.14]