B767 Captain reports being dispatched with an inoperative engine driven generator; with the APU providing the necessary second generator. Enroute the APU experiences auto shutdown several times and crew elects to divert.

Narrative

On a flight from ZZZ to ZZZ1 we were dispatched with the left generator placarded inoperative; which required the APU to be operated throughout the entire flight in accordance with MEL instructions. During cruise; the APU shut down automatically. We restarted it; it ran for approximately 15 minutes; and then it shut down again. We restarted it again. I contacted our Maintenance Department through our Dispatch Department; and was advised that this APU had a history of recent faults. Not wanting to carry a potential electrical problem farther east into the marginal weather of the Midwest and East Coast if the APU continued to shut down and could not be restarted; I elected to make a precautionary divert in the interest of safety. We considered ZZZ3 and ZZZ4 as possible destinations; but the Maintenance Technician advised us that they had no parts available at either station. The Dispatcher suggested ZZZ2; and although it was farther; it was a better option for maintenance and passenger considerations. Since we were not in an emergency situation and needed to burn fuel down to landing weight anyway; I elected to divert to ZZZ2. The aircraft was taken out of service at ZZZ2; the passengers were transferred to another B767 when it became available; and we continued on to ZZZ1.