N.M. Stat. § 72-5-14
The state engineer shall have the power to grant extensions of time in which to complete construction of works, to apply water to beneficial use and for such other reasonable purpose as may in his opinion appear, under any water right application on file in his office, upon proper showing by the applicant of due diligence or reasonable cause for delay. Extensions of time not exceeding five years beyond the time for construction allowed in the original permit, and in no case exceeding a total of ten years after the date of approval of the application, may be granted by the state engineer for construction of works and application of water to beneficial use; provided, that if it shall be made to appear to the state engineer by affidavit of the applicant, his successors or assigns, or by any person for or on behalf of such applicant, and by such other evidence as the state engineer may require, that at least one-fourth of the actual construction work has been completed within such period as extended, the state engineer may, if he is satisfied of the good faith of the applicant and that the project will be to the interest of the development of the state, extend the time for completion of works and application of water to beneficial use for any additional periods he may deem necessary, but not exceeding two years for any one extension, upon such reasonable terms and conditions as he may prescribe; and at the time of granting such extension shall endorse his approval thereon and shall make the proper entry in his records.
NMS § 72-5-14