On January 9, the New Mexico Supreme refused to reconsider Constitution Party of New Mexico v Duran, 34431. The issue is how to interpret section 1-7-2(c) of the election code, and whether a party that submits a petition gets one or two elections. A side issue was that the law, since 2011, requires parties to be notified no later than March of an odd year, if the party is being removed from the ballot. In 2013, the Secretary of State didn’t notify the Constitution Party officers until July that it was being removed, and didn’t notify the party’s registered members until November.
Because the New Mexico Supreme Court merely refused to hear the case, and expressed no opinion, it would be possible for the Constitution Party to re-file in lower state court, or conceivably even federal court. The Green Party is in a similar situation and it could also plausibly sue.