Alternator/CHarging System

6 cyl Front Wheel Drive Automatic

I used my Escape to jump off another vehicle with a severely dead battery. Later that evening my Escape would not start and I had to be jumped off myself. I recharged battery with a charger and it went down again the next day after driving. After recharging the battery with a charger again, I went to AutoZone and they tested the alternator (while on the vehicle) and the battery. The battery checked okay, but the alternator was not charging. I replaced the alternator and recharged the battery with my charger. I then took a trip and the battery went down again. I took the battery to Wal-Mart. They checked it and said it was very low but tested good. I bought a new battery and drove back home and the new battery went down. I went back to Wal-Mart and swapped that battery for another new one. I went back to AutoZone and they tested the alternator (while on the vehicle) and the battery again. Once again the battery checked okay, but the alternator was not charging. The meter was showing only 12, 14V at idle and at 1500rpms. I took the Escape home pulled the alternator off and took it to AutoZone to have it checked off of the vehicle. Test showed that it was working fine putting out 15A.
There are 3 wires to the alternator. The big wire that is connected with a nut and the two small ones in the clip connector. According to the wiring diagram, the big 120A wire and one of the two smaller wires, the 15A, should be hot all the time and they are. The other small wire, the 10A, should only be hot in run or start. I have power in the 120A and the 15A all the time but no power in the 10A anytime.
I know the bulb for the battery/charging system light on the instrument panel works because it comes on when you turn the key on and goes off after you start the motor as do all of the other warning lights. When the Escape is running the battery light NEVER comes on at all. When the battery is about to run out of power, the ABS will sometimes go on and off, the radio will stop working, the A/C blower will slow way down, but the battery light NEVER comes on.