Depends on the type and scale of infringement and gets slightly pedantic: if I can no longer workably exercise my right -- if the infringement is too widespread, say -- do I still have it?
You could sue for everyone for copyright infringement. (This didn't work so well for the RIAA.)
Or you can figure out a way to capitalize off the reason why everyone likes your work.
In any instance you don't lose your copyright.
The two are close, but not synonymous. Take photographs: the exclusive first-use of a photograph is a big thing. If you publish my picture without my permission, my right of control is gone.
I can use copyright laws and the courts to try and get economic redress for that, but nonetheless I no longer have the ability to decide where and when that picture is first published; the ability was stolen from me.
Copyright doesn't prevent copying, it just gives you a way of redress.