They are turned over to the BATF when the dealer closes shop. Also, there's been multiple reports of the BATF coming into "examine the books" and photocopying the store's forms.
That’s why I said “supposedly,” but the difference is that they weren’t designed to be a central database. The so-called “instant background check” is a much worse threat, since those are computerized, and there really isn’t any way to tell how long the government retains them and no way to force them to delete them if they don’t want to.