Replaced alternator, still low voltage

Ford
F150
1998
160000
4.2 L

After the "battery" light came on, I had the alternator checked, which showed a bad alternator. I replaced the alternator, but the light was still on. I took it to the place of purchase and was told it was OK (test was done with the alternator on the truck). By the time I got home, the battery was dead. I had the alternator checked elsewhere, and the voltage was just over 12V. I took it off and went back to place of purchase and a bench test showed the alternator was OK, but no voltage readout was available. When I check the voltage with the engine running, it showed about 12.5 V at the battery. My problem is similar to that of Murdock1 posted Feb 16, 2007.

Any ideas on why the drop from the alternator to the battery?