A319 Captain reported an APU failure in flight with the #2 IDG on MEL. The flight crew requested priority handling and diverted.

Narrative

We were assigned this aircraft for 4 legs on the day of the event. On the first leg to ZZZ the #2 engine generator was producing AC power at 390 Hz. I made an entry in the AML and notified Maintenance. After 2 hours of 'deliberation'; Company Maintenance decided to defer fixing the generator and apply an MEL. We operated the aircraft for the next 3 legs with this MEL; which obviously required the generator to be switched off and the APU to be run continuously. We diligently conducted all pre departure checks required by the MEL on each leg. The MEL also limited the aircraft to MAX FL330. The first 2 legs we flew at FL 270 and 280. On the third leg we were flight-planned for FL320 between ZZZ1 and ZZZ2. Shortly after reaching FL320 the APU Auto Shutdown; leaving us with only a single generator. We immediately requested priority handling and diverted to ZZZ; the nearest suitable airport; for an uneventful landing. It was a very poor decision to leave this aircraft in service with an inoperative IDG. Also; it is clear that our APUs are unreliable; and maintenance decisions based on 'theoretical' APU operational limits are ill-advised and put crews and passengers in an unsafe situation.I will not accept an aircraft with an inoperative engine generator in the future. Application of an MEL that relies on APU operation at cruise altitude is clearly an unacceptable risk.