Did you serve him a 30-day eviction notice (Correct this behavior or get out in 30 days), or did you issue him a 30-day notice of the end of his tenancy?
If he's a month-to-month tenant, a 30 day notice of the end of his tenancy is binding regardless of what monies you accept during that 30 days, but if you accept money after the 30 days, you need to give him notice that it will be applied to his owed balance and does not constitute a new lease.
If you issued an actual 30-day eviction notice based on behavior, severing his lease mid-term, you need to follow it up with a full eviction through the courts. Good luck with that. It's a major pain to evict someone in NH for anything other than non-payment.