N.M. Stat. § 59A-32-15
Conditions for maintaining the discount.
The premium reduction required by this section shall be effective for an insured for a
three-year period after successful completion of the approved course, except that the
insurer may require, as a condition of maintaining the discount, that the insured:
A. not be involved in an accident for which the insured is at fault; and
B. not be convicted or plead guilty or nolo contendere to a moving traffic violation.