Nope, but the store owner’s property rights supersede your 2A rights ON HIS PROPERTY because you don’t have to patronize that store. You have the right to take your business elsewhere.
On HIS property? Yes.
Nothing nullifies your right. But you don't have an absolute right to be on his private property. One right doesn't trump the other. It's that there is no "right" to shop in a given store.
There are a handful of places that post "no carry" signs; malls are usually among them. Your best option is to exercise your right to shop and spend your money elsewhere. A politely worded letter to the owners explaining your decision wouldn't hurt, either.
There is a lot of excellent information about this issue on the Rocky Mountain Gun Owner's website, Merchant Awareness Program(^). Information about what to do, how to approach the business owners, how to react, etc.