Is there any limit to how many times an aircraft evacuation slide may be deployed?
The slide has to be removed from the aircraft completely (generally) and sent back to it's manufacturer to be inspected and repacked, but yes, it can be reused.

This article talks about it in more detail.

As a far as "how many times", I would assume until it breaks ;).  Though honestly, I doubt a slide would ever be deployed more than once, maybe twice in it's life span.