Basically, you told them that, as a contractor, you own the copyright and they’re only buying limited usage rights. When presented that way, most clients balk, even though that’s the way U.S. copyright laws are written.
Some designers, like most photographers and illustrators, only sell usage rights. It’s pretty standard since there’s always the possibility of selling additional rights to other people looking for the same thing. This is much less likely with graphic design since each design is, for the most part, custom made, bespoke and unique to that client’s needs.
In my contracts, I typically include a clause saying that all copyrights for all work belong to me, the seller, until final payment has been made and cleared, at which time the copyright immediately and automatically transfers to the client, the buyer.
I also typically include another clause in the contract saying that I retain certain rights to use the work for self-promotion purposes. Sometimes certain clients object to this or place limitations on it, but they usually don’t care. When they do object to this clause, I’ll gladly change it to meet their demands, but I’ll typically increase the overall price by about five percent citing lost revenue on my part from my inability to use the work for future self-promotion purposes.
For what it’s worth, say away from terms like “reasonable” in contracts. Words like that are open to interpretation and opinion. What’s reasonable to one person isn’t reasonable to another, and it’s this sort of disagreements that lead to bad feelings and attorney’s getting involved. It’s best to use more precise language, as in spelling out exactly what the terms are in tightly defined and unambiguous terms.