Sure they can -Chief can't issue to a PP, ...
they do it all the time.
Plenty of guys get denied for being PP's on renewal,
even when the disqualifying offense predates the original LTC.
They didn't mention the old disqualification the first time around,
and then the vintage courthouse records get digitized,
and the renewal checkup fails.
Plus, Falmouth PD (for one) even has a form letter stating that
just because we gave you an FID
doesn't mean you're allowed to use it.