Airliners use generally two likelihoods of a failure: once in a billion hours for events which can bring down the plane and once in 10 million hours for events

Airliners use generally two likelihoods of a failure: once in a billion hours for events which can bring down the plane and once in 10 million hours for events which don't take it down alone, but a combination of those can. The problem with the batteries is that they were certified to fail once in ten million hours but failed twice in 50000 hours. If both engines fail (unlikely, but it can happen -birdstrikes, fuel contamination, it is one of the 10 million events), you need the main battery for powering avionics (if it fails you're screwed) until APU is started and providing power (you have about 10 minutes, 2 APU start attempts). The APU battery is needed to start the APU. Unfortunately, APU has fire protection which needs power to run, which is drawn from the APU battery. So if APU battery fails at any time after APU start, the system will shut the APU down and you'll lose all the power.