Are you sure the alt. is charging correctly ?, these default to about 13.5 volts if the alternator is faulty which can mislead. These systems can charge up to about 16v under PCM control and batt temp/state of charge etc.

I have got a smart system tester from Vectron that plugs into the 3 pin plug and simulates the signals to/from the PCM, it drives the alternator right up to full charge voltage thereby proving alt. fault or not.