Here's a quick run down on how a car's charging system works:
In your case, if you have 12.6 volts running, your battery WILL die shortly. With that said, I would check the Alternator (yes, I know you have replaced it, but rebuilt alternators are not that great but you CAN test them easy enough, or your local auto parts store will test it for free), the Regulator (I think on that year it still was on the firewall and external), the cables/wires especially the GROUND wire (the BLACK one). I remember once going through 4 Regulators to get one that worked on my 1973 Dodge. Sorry I can't be more helpful, my old Dodge brain just isn't ani't what it used to be.
Either the alternator is not putting out or it thinks the battery is full and won't charge. I highly suspect a bad ground or a Regulator. You can run "cheater" cords (wires) from the ground to the Regulator (black side of the battery to the firewall <regulator>) etc, and see if the voltage changes. If it goes to 13.5 volts, you know you have a loose or broken wire somewhere.
By the way, I would check all the fuses, just to be safe. It ony take 5 mins. Was this working just fine an it up'd and died or were you working on something (electrical)?