I'm not familiar with overwater/ETOPS procedures, but here's my 1.5 cents:
If the APU were running during the flight (which is sounds like it was, or else no reason for reroute), it would have been running for a reason. On my airplane, 1 main generator can be deferred. If that is the case, the APU must be kept running for the duration of the flight for electrical redundancy (1 generator can handle the entire airplane just fine, you just don't want to be reliant on only 1 generator).
So, what may have happened is the APU shut down for some reason during flight.
Once again, that is pure speculation. But if that were the aircraft that I fly, and we had a generator deferred and the APU shutdown mid-flight, we are required to land at nearest suitable airport.