FIFTH AMENDMENT TO LETTER OF CREDIT FACILITY AGREEMENT AND AMENDMENT TO OTHER LOAN DOCUMENTS

Exhibit 10.4

FIFTH AMENDMENT TO

LETTER OF CREDIT FACILITY AGREEMENT AND

AMENDMENT TO OTHER LOAN DOCUMENTS

THIS FIFTH AMENDMENT TO LETTER OF CREDIT FACILITY AGREEMENT AND AMENDMENT TO OTHER LOAN DOCUMENTS (the “Fifth Amendment” or this “Amendment”), effective as of the 21^st day of December, 2012 (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”), the Lenders party hereto (the “Lenders”) and CAPITAL ONE, N.A., as Administrative Agent for 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 and that Fourth Amendment to Letter of Credit Facility Agreement and Waiver dated November 8, 2012 (as amended and as may be further amended, restated, supplemented or modified from time to time, the “Credit Agreement”); and

WHEREAS, the Borrower has requested the Lenders and the Administrative Agent extend the Maturity Date (as defined in the Credit Agreement); and

WHEREAS, the Administrative Agent and the Lenders are willing to so amend the Credit Agreement, subject to the terms and conditions set forth herein.

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. Amendment to Maturity Date. (a) The definition of “Maturity Date” in Section 1.02 of the Credit Agreement is hereby deleted and the following is substituted therefor:

““Maturity Date” means March 24, 2014.

3. 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’ or Lenders’

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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 Guarantor under or pursuant to the Credit Agreement or any of the other Loan Documents or entitle Borrower and/or 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: (i) default or Event of Default that may exist under the Credit Agreement or under any other Loan Document; (ii) term, provision, condition, covenant or agreement contained in the Credit Agreement or in any of the other Loan Documents; or (iii) 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.

4. 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.

5. Representations and Warranties. The Borrower and Guarantors hereby represent and warrant to the Administrative Agent and the Lenders that (a) this Amendment has been duly executed and delivered on behalf of the Borrower and Guarantors, (b) this Amendment constitutes a valid and legally binding agreement enforceable against the Borrower and Guarantors in accordance with its terms, subject 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, (c) 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, (d) except as waived in Section 4 hereof, no Default or Event of Default exists under the Credit Agreement or under any Loan Document and (e) the execution, delivery and performance of this Amendment has been duly authorized by the Borrower and Guarantors.

6. 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:

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7. 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.

8. Governing Law. This Amendment, the other Loan Documents 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.

9. 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.

10. References. The words “hereby,” “herein,” “hereinabove,” “hereinafter,” “hereinbelow,” “hereof,” “hereunder” and words of similar import when used in this Amendment

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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.

11. 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.

12. Release by Borrower and Guarantors. 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 (i) arising directly or indirectly out of the Credit Agreement, Loan Documents, or any other documents, instruments or any other transactions relating thereto and/or (ii) 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.

13. 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.