LIMITED WAIVER AND SEVENTH AMENDMENT TO LETTER OF CREDIT FACILITY AGREEMENT

Exhibit 4.40

LIMITED WAIVER AND SEVENTH AMENDMENT TO LETTER OF CREDIT FACILITY AGREEMENT

THIS LIMITED WAIVER AND SEVENTH AMENDMENT TO LETTER OF CREDIT FACILITY AGREEMENT (the “Amendment”), dated to be effective as of April 10, 2013 (the “Amendment Effective Date”), is entered into by and among BLACK ELK ENERGY OFFSHORE OPERATIONS, LLC, a Texas limited liability company (the “Borrower”), the Guarantors party hereto (the “Guarantors”), CAPITAL ONE, N.A., as Administrative Agent for the Lenders (“Administrative Agent”) and the Lenders signatory hereto (the “Lenders”).

RECITALS

WHEREAS, the Borrower, the Lenders and the Administrative Agent entered into that certain Letter of Credit Facility Agreement dated December 24, 2010 as amended by that First Amendment to Letter of Credit Amendment dated May 31, 2011, that Second Amendment to Letter of Credit Facility Agreement dated December 30, 2011, that Third Amendment to Letter of Credit Facility Agreement dated May 24, 2012, that Fourth Amendment to Letter of Credit Facility Agreement and Waiver dated November 8, 2012, that Fifth Amendment to Letter of Credit Facility Agreement dated December 20, 2012 and that Sixth Amendment to Letter of Credit Facility dated February 22, 2013 (as further amended, restated, supplemented or modified from time to time, the “Credit Agreement”);

WHEREAS, the Borrower has requested that the Administrative Agent and Lenders (i) waive compliance with certain covenants in the Credit Agreement and (ii) amend certain other provisions as set forth herein; and

WHEREAS, the Lenders and the Administrative Agent have agreed to provide such waivers and amendments as reflected in this Amendment, subject to the terms and conditions herein, and provided that the Borrower and the Guarantors ratify and confirm all of their respective obligations under the Credit Agreement and the Loan Documents.

NOW, THEREFORE, in consideration of the foregoing and the mutual covenants set forth in this Amendment, the Borrower, the Guarantors, the Lenders and the Administrative Agent agree as follows:

1. Defined Terms. Unless otherwise defined herein, capitalized terms used herein have the meanings assigned to them in the Credit Agreement.

2. Limited Waiver. Subject to the terms and conditions set forth herein, the Administrative Agent and the Lenders hereby waive any Event of Default arising under the Credit Agreement as a result of (a) the failure of the Borrower to comply with Section 9.01(c) of the Credit Agreement as of and for the fiscal quarter ended December 31, 2012, (b) the failure of the Borrower to comply with the covenant contained in Section 9.17 of the Credit Agreement as it relates to existing oil hedges but only to the extent required to avoid an Event of Default and only for the calendar month of January 2013, (c) the failure of the Borrower to comply with the covenant contained in Section 9.17 of the Credit Agreement as it relates to existing oil hedges but only to the extent that such noncompliance is a result of the sale of certain oil and gas properties to Renaissance Offshore, LLC, only to the extent required to avoid an Event of

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Default, and provided Borrower is in compliance with such covenant on May 31, 2013, when such covenant shall be retested. The waivers set forth in this Section 2 (the “Default Waiver”) are limited to the extent specifically set forth in (a), (b), and (c) above and no other terms, covenants or provisions of the Credit Agreement or any other Loan Document are intended to be affected hereby. The Default Waiver is granted only with respect to the failure of the Borrower to comply with Section 9.01(c) as of and for the fiscal quarter ended December 31, 2012, and the Borrower’s violation of Section 9.17 with respect to the overhedged oil position for the calendar month of January 2013 and as a result of the Renaissance Sale and shall not apply to any violation of Section 9.01(c) with respect to any fiscal quarter other than the fiscal quarter ended December 31, 2012, with respect to any other violation of Section 9.17, or any actual or prospective default or violation of any other provision of the Credit Agreement or any other Loan Document. The Default Waiver shall not in any manner create a course of dealing or otherwise impair the future ability of the Administrative Agent or the Lenders to declare a Default or Event of Default under or otherwise enforce the terms of the Credit Agreement or any other Loan Document with respect to any matter other than those specifically and expressly waived in the Default Waiver.

3. Amendment to Credit Agreement. The Credit Agreement is hereby amended as follows:

(a) Section 9.01(a) is hereby deleted and the following is substituted therefore:

“(a) Payables Restriction. The Borrower will not permit, at any time, its accounts payable over ninety (90) days old to exceed $6,000,000 in the aggregate; provided Borrower may exclude from the calculation of this covenant accounts payable owed to or for (i) legal fees owed to Persons other than counsel to Administrative Agent and the Lenders, (ii) joint interest billings, (iii) Grand Isle Shipyard and (iv) Gulf Offshore Logistics (clauses (i) through (iv) are collectively referred to herein as, the “Excluded Payables”). Notwithstanding anything contained in the Credit Agreement to the contrary, on or before the close of business on the first Business Day of each calendar week, Borrower shall deliver to Administrative Agent a certificate in form and substance acceptable to Administrative Agent (i) setting forth reasonably detailed calculations demonstrating compliance with Section 9.01(a) including details of the Excluded Payables, (ii) certifying as to whether a Default has occurred with respect to this financial covenant and (iii) attaching a schedule of the aging payables listing those included in the calculation and the Excluded Payables. Notwithstanding the provisions of Section 10.01 of the Credit Agreement, it shall be an Event of Default if Borrower fails to comply with the covenant set forth herein for two (2) consecutive weeks.”

(b) Notwithstanding Section 9.01(b) of the Credit Agreement, the parties hereby agree that for the fiscal quarter ending March 31, 2013 the Borrower will not permit, as of the last day of such fiscal quarter, its ratio of (i) Consolidated EBITDAX of the Borrower and the Restricted Subsidiaries for the trailing four quarter period then ended to (ii) Consolidated Interest Expense paid by the Borrower during such period and the Restricted Subsidiaries to be less than 2.25 to 1.00. The foregoing amendment to Section 9.01(b) relates solely to the fiscal quarter ended March 31, 2013 and to no other period of time.

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(c) Notwithstanding Section 9.01(c) of the Credit Agreement, the parties hereby agree that for the fiscal quarter ending March 31, 2013 the Borrower will not permit, as of the last day of such fiscal quarter, its ratio of (i) total Debt of the Borrower and the Restricted Subsidiaries as of such date to (ii) Consolidated EBITDAX of the Borrower and the Restricted Subsidiaries for the trailing four quarter period then ended to exceed 3.50 to 1.00. The foregoing amendment to Section 9.01(c) relates solely to the fiscal quarter ended March 31, 2013 and to no other period of time.

(d) Notwithstanding anything contained in the Credit Agreement to the contrary, the parties acknowledge and agree that Borrower’s compliance with Section 9.17 of the Credit Agreement shall be tested on May 31, 2013 and Borrower agrees to deliver to Administrative Agent a certificate in form and substance acceptable to Administrative Agent (i) setting forth reasonably detailed calculations demonstrating compliance with Section 9.17 of the Credit Agreement and (ii) certifying as to whether a Default has occurred with respect to this covenant.

4. Reservation of Rights. Nothing contained in this Amendment is intended to limit, nor shall it be deemed to limit or in any way affect, any of the Administrative Agent’s or Lenders’ claims, rights or remedies under the Credit Agreement or any of the other Loan Documents, and nothing in this Amendment shall in any way modify, change, impair, affect, diminish, or release any liability of Borrower and/or any Guarantor under or pursuant to the Credit Agreement or any of the other Loan Documents or entitle Borrower and/or any Guarantor to any other or further notice or demand whatsoever. Nothing contained herein, nor any failure by the Administrative Agent or any Lender to exercise any of its rights or remedies under the Credit Agreement or any of the other Loan Documents, shall be deemed to constitute, nor is it intended to constitute, any waiver whatsoever of any: (a) Default or Event of Default that may exist under the Credit Agreement or under any other Loan Document; (b) term, provision, condition, covenant or agreement contained in the Credit Agreement or in any of the other Loan Documents; or (c) rights or remedies of the Administrative Agent or any Lender under the Credit Agreement or any of the other Loan Documents, at law or in equity or otherwise, or prejudice or preclude any other or further exercise of any such right or remedy by the Administrative Agent or the Lenders, all of which are hereby reserved.

5. Ratification. The Borrower and Guarantors hereby ratify all of their respective Obligations under the Credit Agreement and each of the Loan Documents to which it is a party, and agrees and acknowledges that the Credit Agreement and each of the Loan Documents to which it is a party are and shall continue to be in full force and effect as amended and modified by this Amendment. Nothing in this Amendment extinguishes, novates or releases any right, claim, lien, security interest or entitlement of any of the Lenders or the Administrative Agent created by or contained in any of such documents, nor is the Borrower nor any Guarantor released from any covenant, warranty or obligation created by or contained herein or therein.

6. Representations and Warranties.

(a) The Borrower and Guarantors hereby represent and warrant to the Administrative Agent and the Lenders that (i) this Amendment has been duly executed and delivered on behalf of the Borrower and Guarantors, (ii) this Amendment constitutes a valid and legally binding agreement enforceable against the Borrower and Guarantors in accordance with its terms, subject

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to applicable bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium or other laws affecting creditors’ rights generally and subject to general principles of equity, regardless of whether considered in a proceeding in equity or at law, (iii) the representations and warranties contained in the Credit Agreement and the Loan Documents are true and correct on and as of the date hereof in all material respects as though made as of the date hereof, (iv) no Default or Event of Default exists under the Credit Agreement or under any Loan Document and (v) the execution, delivery and performance of this Amendment has been duly authorized by the Borrower and Guarantors.

(b) The Borrower hereby (i) represents and warrants to the Administrative Agent and the Lenders that the execution of this Amendment does not violate the terms of (A) the Indenture, (B) the Second Lien Intercreditor Agreement, (C) the W & T Intercreditor Agreement or (D) the BP Intercreditor Agreement (collectively, the “Intercreditor Agreements”) and (ii) covenants, represents and warrants that no consent is required under any Intercreditor Agreement for the Borrower, Administrative Agent or the Lenders to execute this Amendment.

7. Conditions to Effectiveness. This Amendment shall be effective on the Amendment Effective Date only if the following are satisfied on or before such Amendment Effective Date:

(a) the receipt by the Administrative Agent of this Amendment fully executed by all parties hereto;

(b) the payment to the Administrative Agent of all fees that are due, including all expenses of Administrative Agent and the Lenders in connection with this Amendment and any billed fees and disbursements of Andrews Kurth LLP, in connection with this Amendment; and

(c) the receipt by the Administrative Agent of such other documents as the Administrative Agent or its special counsel may reasonably request.

8. Counterparts. This Amendment may be signed in any number of counterparts, which may be delivered in original or facsimile form each of which shall be construed as an original, but all of which together shall constitute one and the same instrument.

9. Governing Law. This Amendment and all other documents executed in connection herewith shall be deemed to be contracts and agreements under the laws of the State of Texas and of the United States of America and for all purposes shall be construed in accordance with, and governed by, the laws of Texas and of the United States.

10. Continuing Effect of the Credit Agreement. This Amendment shall not constitute a waiver of any provision not expressly referred to herein and shall not be construed as a consent to any action on the part of the Borrowers or Guarantors that would require a waiver or consent of the Lenders or an amendment or modification to any term of the Loan Documents except as expressly stated herein. Except as expressly modified hereby, the provisions of the Credit Agreement and the Loan Documents are and shall remain in full force and effect.

11. References. The words “hereby,” “herein,” “hereinabove,” “hereinafter,” “hereinbelow,” “hereof,” “hereunder” and words of similar import when used in this Amendment shall refer to this Amendment as a whole and not to any particular article, section or provision of this Amendment. References in this Amendment to an article or section number are to such articles or sections of this Amendment unless otherwise specified.

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12. Headings Descriptive. The headings of the several sections and subsections of this Amendment are inserted for convenience only and shall not in any way affect the meaning or construction of any provision of this Amendment.

13. Release by Borrower and Guarantors. The Borrower and each Guarantor does hereby release and forever discharge the Administrative Agent and each of the Lenders and each affiliate thereof and each of their respective employees, officers, directors, trustees, agents, attorneys, successors, assigns or other representatives from any and all claims, demands, damages, actions, cross-actions, causes of action, costs and expenses (including legal expenses), of any kind or nature whatsoever, whether based on law or equity, which any of said parties has held or may now or in the future own or hold, whether known or unknown, for or because of any matter or thing done, omitted or suffered to be done on or before the actual date upon which this Amendment is signed by any of such parties (a) arising directly or indirectly out of the Credit Agreement, Loan Documents, or any other documents, instruments or any other transactions relating thereto and/or (b) relating directly or indirectly to all transactions by and between the Borrower or Guarantors or their representatives and the Administrative Agent and each Lender or any of their respective directors, officers, agents, employees, attorneys or other representatives and, in either case, whether or not caused by the sole or partial negligence of any indemnified party. Such release, waiver, acquittal and discharge shall and does include, without limitation, any claims of usury, fraud, duress, misrepresentation, lender liability, control, calling of the Credit Agreement into default, exercise of remedies and all similar items and claims, which may, or could be, asserted by any of the Borrower or Guarantors.

14. Final Agreement of the Parties. THIS AMENDMENT, THE CREDIT AGREEMENT 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 AMONG THE PARTIES.

[Signature Pages Follow]

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be executed by their respective officers thereunto duly authorized as of the date first above written.

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