In today's world of auto parts stores, it's not uncommon AT ALL to get a bad unit right out of the box. They are "rebuilt" (and I use the term very loosely) for next-to-nothing, and with labor that gets paid about the same.
Typical wisdom on the Ford boards is to take yours to your town's "reputable rebuilder" and have him go through your old one. Far better, long-lasting results are to be had that way.
Life-time guarantee? Sure! They couldn't sell that crap at all without one!
The only thing I can add, assuming your "new" alternator is really OK, is that Ford uses a fuse (usually 5-amps) in the field wire. Look in your Owner's Manual to find which one it is.
Oh, and rarely (but sometimes) the small connector on the alternator has pins that get loose with the constant vibration. They lose their "tension" and you end up with a bad or intermittent connection. The connectors are available separately to enable you to splice a new one in place if that's the case.
But I'd be first looking for a bad out-of-box unit.
Ford 6G alternators are good units, but the domestic parts-house rebuilds are usually crap.
2004 Terry 250RKS, perfect for the two of us and the pups. It recently replaced our Flagstaff 21FB.
2000 F-350 7.3L CC/LB 4WD Lariat 3:73's