B767 Captain reported on preflight the APU failed twice resulted in aircraft refusal due to ETOP requirement.

Narrative

During preflight; an APU GEN OFF EICAS came on and the generator went offline. The APU GEN OFF QRH was accomplished; and the generator reset with 1 attempt. Approximately 5 minutes later; the APU performed an auto shutdown. The First Officer and I discussed the situation with Maintenance Control and Dispatch; and agreed a refusal was appropriate with 2 back to back APU malfunctions and the APU required for 180 minute ETOPS. We then asked Maintenance Control to trouble shoot the APU to determine the cause of the auto shutdown.