N.M. Stat. § 19-8-19
The record owners or owner of any mineral lease or approved assignment thereof heretofore issued by the commissioner and maintained in good standing may enter into a stipulation with the commissioner of public lands making the terms and conditions of this act [19-8-18, 19-8-19 NMSA 1978] a part of any such existing lease, the same as if said provisions had been a part of said lease when issued. The commissioner may charge a fee not to exceed ten dollars ($10.00) for the filing and recording of such stipulation.
Provided, further, that if for any reason beyond the control of the lessee production of minerals in paying quantities shall cease after the secondary term has expired, the producing lessee may, with the written permission of the commissioner, continue said lease in operation and effect from year to year for an additional period not to exceed three (3) years by continued payment in advance of annual rentals at the rate provided in the secondary term of the lease.
NMS § 19-8-19