N.M. Stat. § 61-1-15
If a person who has requested a hearing does not appear and no continuance has been granted, the board or hearing officer may hear the evidence of such witnesses as may have appeared, and the board may proceed to consider the matter and dispose of it on the basis of the weight of the evidence before it in the manner required by Section 61-1-13 NMSA 1978. Where, because of accident, sickness or other extraordinary cause, a person fails to request a hearing or fails to appear for a hearing that the person has requested, the person may within a reasonable time apply to the board to reopen the proceeding, and the board upon finding such cause sufficient shall immediately fix a time and place for hearing and give the person notice as required by Sections 61-1-4 and 61-1-5 NMSA 1978. At the time and place fixed, a hearing shall be held in the same manner as would have been employed if the person had appeared in response to the original notice of hearing.
NMS § 61-1-15