AMENDMENT NO. 4 TO SECOND AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP OF ATLAS PIPELINE PARTNERS, L.P.

Exhibit 10.2(e)

AMENDMENT NO. 4

TO

SECOND AMENDED AND RESTATED AGREEMENT OF LIMITED

PARTNERSHIP

OF

ATLAS PIPELINE PARTNERS, L.P.

THIS AMENDMENT NO. 4 TO SECOND AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP OF ATLAS PIPELINE PARTNERS, L.P. (this “Amendment”), dated as of June 12, 2008, is entered into and effectuated by Atlas Pipeline Partners GP, LLC, a Delaware limited liability company (the “General Partner”) and the general partner of Atlas Pipeline Partners, L.P., a Delaware limited partnership (the “Partnership”), pursuant to authority granted to it in Section 13.1 of the Second Amended and Restated Agreement of Limited Partnership of the Partnership, dated as of March 9, 2004, as amended (the “Limited Partnership Agreement”). Capitalized terms used but not defined herein are used as defined in the Limited Partnership Agreement.

WHEREAS, Section 13.1(d) of the Limited Partnership Agreement provides that the General Partner, without the approval of any Partner or Assignee, may amend any provision of the Limited Partnership Agreement to reflect a change that, in the discretion of the General Partner, does not adversely affect the Limited Partners in any material respect, and the General Partner has determined that the amendment contemplated hereby does not adversely affect the Limited Partners in any material respect; and

WHEREAS, Section 7.10 (a) of the Limited Partnership Agreement provides that, (i) whoever a potential conflict of interest exists or arises between, inter alia, the General Partner and the Partnership, any Partner or Assignee, any resolution or course of action by the General Partner shall be permitted and deemed approved by all Partners, and shall not constitute a breach of the Limited Partnership Agreement or of any duty stated or implied by law or equity, if the resolution or course of action is, or by operation of the Limited Partnership Agreement is deemed to be, fair and reasonable to the Partnership, and (ii) any resolution of the conflict of interest shall be conclusively deemed to be fair and reasonable to the Partnership if such resolution is approved by Special Approval, and such Special Approval has been obtained; and

WHEREAS, the General Partner deems it in the best interest of the Partnership to effect this Amendment.

NOW, THEREFORE, it is hereby agreed as follows:

A. Amendment. Section 1.1 of the Limited Partnership Agreement is hereby amended to amend and restate the following definition:

“Operating Surplus” means, with respect to any period ending prior to the Liquidation Date, on a cumulative basis and without duplication,

(a) the sum of (i) all cash and cash equivalents of the Partnership Group on hand as of the close of business on the Initial Closing Date, (ii) all cash receipts of the Partnership Group for the period beginning on the Initial Closing Date and ending with the last day of such period, other than cash receipts from Interim Capital Transactions (except to the extent specified in Section 6.5) and (iii) all cash receipts of the Partnership Group after the end of such period but on or before the date of determination of Operating Surplus with respect to such period resulting from Working Capital Borrowings, less

(b) the sum of (i) Operating Expenditures for the period beginning on the Initial Closing Date and ending with the last day of such period and (ii) the amount of cash reserves that is necessary or advisable in the reasonable discretion of the General Partner to provide funds for future Operating Expenditures.

For the purposes of determining Operating Surplus, there shall be excluded from the calculation thereof any payments made or received, or charges incurred, including premiums or penalties paid, in connection with the breakage, termination or unwinding of any hedging agreement before its scheduled termination or expiration date. As used herein, the term “hedging agreement” means any commodity, interest rate or currency swap, cap, floor, collar, forward agreement or other exchange or protection agreement or any option with respect to any such transaction.

Notwithstanding the foregoing, “Operating Surplus” with respect to the Quarter in which the Liquidation Date occurs and any subsequent Quarter shall equal zero.

B. Agreement in Effect. Except as hereby amended, the Limited Partnership Agreement shall remain in full force and effect.

C. Applicable Law. This Amendment shall be construed in accordance with and governed by the laws of the state of Delaware, without regard to principles of conflicts of laws.

D. Invalidity of Provisions. If any provision of this Amendment is or becomes invalid, illegal or unenforceable in any respect, the validity, legality and enforceability of the remaining provisions contained herein shall not be affected thereby.

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

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