You might want to start by enabling auditing on the server, then log all events happening (successes and fails) to those printers. Worst case scenario could be that someone is goofing off and deliberately deleting those printers to mess with your users.
Even if this is not the case, the logging might tell you when you're losing the printers, so that you have a point of reference to check the rest of the system. That way, you could tell if a certain events are corrupting the print ports or altering them in some way.
Catadmin - New to Server Admin, but willing to learn... All help is appreciated.