Have the alternator bench tested. There is definitely a problem with it somewhere.
The alternator is fine. Also, there have been three alternators on the car since this problem started occurring when I acquired the car 10 years ago; the original alternator and then two new ones. The newest one is only a couple of weeks old, as I was thinking the same thing you are, that the alternator was bad. That would be some extremely bad luck if all three were duds