We bought a vacation package with a resort for which we pay a yearly maintanance fee; what can they do if we don't pay it?

If you don't pay the maintenance fee, the resort could file a lawsuit against you for breach of contract.  If you are in breach of contract, the resort would no longer be bound by the terms of the contract and would no longer honor its terms.  You would forfeit your right to utilize the vacation package and depending on the terms of the contract, your ownership of the points you referenced would probably be terminated. There may be language in the provisions of the contract allowing the resort to recover reasonable attorney fees in the event of litigation.