charging problem!

[broncoking351]

i have a 2003 f-250 with the 6.0 and i cant seem to figure out my charging problem. i went out to leave for work and the truck was stone dead. i jumped it and it ran all day with no problems. i parked it for a few hours and went to start it and it started no problem. went back 20 minutes later and it was dead. i pulled the alternator off and went to autozone and had it tested and it tested good four times. i then pulled out the batteries and they were both bad. i put two new batteries in and both batteries were holding 12.2 to 12.6 volts not running then while the truck ran the alternator was only showing putting out 12.2 volts at idle, at 2000 rpms it put out 13.2 to 13.4 volts. i bought a new alternator and it put out the same volts. i checked the fusible links and wires and they all seemed to bwe good . im stuck and at a loss! if anyone has any ideas id appreciate it! thank you