B757-200 WAS DISPATCHED WITH ONE GENERATOR INOP. APU WAS UTILIZED FOR SECOND GENERATOR; BUT FAILED DURING NIGHT FLT. EMER WAS DECLARED.

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THE AIRPLANE WE STARTED THE DAY WITH HAD A WRITE-UP THAT THE R GENERATOR 'DRIVE' LIGHT WAS FLICKERING ON AND OFF. THE R GENERATOR DRIVE WAS DISCONNECTED BY MAINT AND DEFERRED. WE AGREED TO TAKE THE AIRPLANE AND KEEP THE APU RUNNING DURING THE ENTIRE FLT TO PROVIDE A SECOND GENERATOR. THE WX IN ZZZ1 WAS FORECAST TO BE VFR AND THE DAY FLT TO ZZZ1 WAS UNEVENTFUL. ARRIVING AT ZZZ1 THE GPU WAS UNAVAILABLE AND THE APU CONTINUED TO RUN. ON THE FLT BACK TO ZZZ FROM ZZZ1 AT FL350 AND APPROX 150 MI W OF ZZZ THE APU 'FAULT' LIGHT CAME ON AND THE APU SHUT DOWN. AT THIS POINT THE APU HAD BEEN RUNNING FOR APPROX 8 HRS. THE APU FAULT CHKLIST WAS RUN AND AN ATTEMPT WAS MADE TO RESTART THE APU; BUT THE RESTART WAS UNSUCCESSFUL. DISPATCH WAS CALLED. WX WAS PULLED UP FOR BOTH ZZZ AND ZZZ2. BY THIS POINT THE ACFT WAS 80-90 MI W OF ZZZ AND IT WAS DECIDED THAT A NORMAL DSCNT INTO ZZZ WOULD TAKE NO LONGER THAN TURNING BACK AROUND AND HAVING TO SPIRAL DOWN TO ZZZ2. AN EMER WAS DECLARED WITH CTR AND PRIORITY HANDLING WAS REQUESTED. THE WX AT ZZZ WAS 3000 FT BROKEN AND 3 MI VISIBILITY. AN UNEVENTFUL ILS APCH WAS ACCOMPLISHED AND THE AIRPLANE WAS TAXIED TO THE GATE WITH NO FURTHER PROBS. FURTHER CHKS BY MAINT ONCE THE ACFT WAS AT THE GATE INDICATED THAT THE APU AUTO SHUTDOWN BECAUSE OF LOW OIL QUANTITY.