AN A320 WITH AN ENG GENERATOR MEL'ED EXPERIENCED AN APU AUTOMATIC SHUTDOWN AND DIVERTED TO AN ENRTE ALTERNATE STATION.

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WE WERE DISPATCHED WITH THE #2 ENG GENERATOR DEFERRED. THIS REQUIRED THE APU TO OPERATE THROUGHOUT THE FLT AND LIMITED THE MAX ALT TO FL330. 10 MINS AFTER REACHING OUR ASSIGNED CRUISE ALT OF FL320; THE APU AUTOMATICALLY SHUT DOWN. WE WERE ABLE TO RESTART THE APU ON THE FIRST ATTEMPT. AFTER ALLOWING IT TO STABILIZE; WE WERE ABLE TO SELECT THE APU GENERATOR BACK ONTO THE ELECTRICAL BUS SUCCESSFULLY ON THE FIRST ATTEMPT. WE NOTIFIED DISPATCH AND MAINT VIA ACARS AND SUBMITTED THE APPROPRIATE RPT VIA ACARS. CHKING CFDS CURRENT LEG RPT; WE NOTED MULTIPLE 'HITS' FOR THE APU FUEL CTL UNIT. 13 MINS LATER; THE APU AUTOMATICALLY SHUT DOWN AGAIN. BEING LEFT WITH A SINGLE MAIN ELECTRICAL SOURCE; THE APU BEING UNRELIABLE AND THE IDG ON #2 ENG DISCONNECTED PER THE MEL; WE IMMEDIATELY DIVERTED INTO ZZZ1 WHICH WAS DIRECTLY AHEAD OF US ON OUR RTE. WE COORD THE DIVERT WITH DISPATCH AND MAINT. THE WX WAS CLR AND ATC ALLOWED US TO PROCEED DIRECTLY TO ZZZ1. FLT ATTENDANTS AND PAX WERE NOTIFIED. I USED MY EMER AUTH TO LAND OVERWT PER FLT MANUAL. BECAUSE IT WAS DAY VMC AND ATC CLRED US DIRECT TO ZZZ1 WITH NO DELAYS; SEQUENCING; OR VECTORS; I ELECTED NOT TO DECLARE AN EMER PER FOM EMER CHAPTER GUIDANCE IN THE SECTION ON OVERWT LNDG. THE LNDG WAS VERY SMOOTH WITH MINIMAL SINK RATE (LESS THAN 200 FPM) AND NO SIDELOADS. THE OVERWT LNDG WAS RPTED THROUGH ACARS RPT. MAINT WAS NOT ABLE TO REPAIR THE ACFT EVEN BY THE EVENING OF THE FOLLOWING DAY.