The laws of your state will control your options, but in Pennsylvania, you would be able to have them register you as a nonconforming use, and you would be able to continue the use because you were there storing the RV before the zoning regulation was no the books. Here, the towship supervisors or borough council passes the law, the zoning officer enforces the law, and the zoning hearing board is the appeals board.
They would have been more effective passing a stand-alone ordinance controlling all commercial vehicles over a certain gross vehicle weight, but the legalities aren't the same everywhere, and it might be a very enforceable law there.
I would approach them indicating my concern and try to convince them to modify the law to prevent the parking of unregistered vehicles instead. That way, if people were parking junkers and running down the neighborhood, they would have recourse, but it wouldn't effect active RVr's use. There was probably some cause for the regulation. Trying to find out why they made the law in the first place, then coming up with a solution might be easier.
Are they regulating all vehicles like boats and landscaper's trailers also, or just RV's?