B737-700
Flight Crew Last 90 Days 438
Time Pressure; Workload
Aircraft Equipment Problem Critical
Flight Crew Landed in Emergency Condition; Flight Crew Diverted
Aircraft
We started the day with the #2 generator not connecting after engine start.  It was then MEL'd so we had to use the APU in flight.  On our fourth leg; (ZZZ to ZZZ1) during the climb to FL410; the APU shutdown disconnecting the autopilot and leaving us with only the #1 generator.  We ran checklists; coordinated with Dispatch and contacted ATC with intentions.  We diverted to ZZZ2 [advised ATC] (since we were unsure why the APU shutdown) and landed without incident.
A B737 pilot reported that after being dispatched with an inoperative engine driven generator; the APU shut down in flight for an unknown reason; which necessitated a divert due to single generator operation.