Thats not a good idea. The case is designed to bring air in and remove air out if properly setup. Getting two years of service out a gpu is not bad. Maybe someone else can jump in but it sure sounds like your card is dying.
One thing I would do is check your GPU and maybe reapply some thermal paste to see if that helps. Underneath that fan is a heatsink much like a cpu. It might help and be worth a try. If you have not done that before, I would start another forum and request help on removing and reapplying paste to a GPU