Death or your remarriage are the standard conditions upon which a spousal maintenance obligation would end (short of a defined time period). Some parties negotiate for additional conditions on the maintenance, such as cohabitation.
If your decree does not set forth such a terminating condition then you should seek to enforce the decree, perhaps by hiring an attorney and seeking an award of fees for having to enforce the decree. This is especially the case if his basis for ceasing payment is your alleged "cohabitation".
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