Jeep battery or alternator dead?

[GilpinGuy]

I'm pretty good under the hood, but this has me stumped. Intermittently, when I start the 99 Wrangler (4.0) it acts like the battery is almost dead. I hook up the handy dandy battery tester (engine off) and it shows full charge. I start the engine and the tester says alternator is charging at 100%.

I put in a Napa remanufactured alternator last summer and the battery is 2 years old. WTF is going on here? What's wierd is that it's intermittent.

ETA: I already cleaned the battery terminals and the connections to the alternator look clean.