Update. I had the alternator checked at an alternator rebuild shop. They say the alternator is working fine. So, that's not the problem. The only other thing in the charging circuit is the voltage regulator. So, if the alternator is fine, then the problem has to be the regulator. Is that correct? Is there anything else that could be causing the battery to continue to discharge every time it is driven?

I figure if I just buy a new 110 amp one wire alternator the cost is about the same, plus I eliminate the old voltage regulator from the charging circuit.

What do you think?