Starting and running problems...please help!!

So a little history...my mother-in-law recently left her dome light or whatever on overnight....drained the battery and pretty much wasted it beyond being able to be charged, even with a trickle charger left on it for days. Got it back up and running for a week or so and she started noticing it acting funny with the lights and accessories running. Eventually it started dying on her in traffic. She had it towed to my place and I pulled the alternator and took it in to have it tested and it passed...weird. Okay, so I put the alternator back in and cleaned and tightened all the connections and sent her on her way. Ran fine for a day or two, then it died again in traffic. We limped it to Autozone and they tested the battery and said it was at 2%. Wasted! So we bought a new battery and put that in and it worked great a couple more days....now its back in my driveway with a dead battery again...bummer! Could the part store be mistaken the alternator was good? They tested it twice to be sure. Is there maybe something drawing amps while the keys off? My multimeter recently took a crap on me but I do have a good test light...If someone can just point me in the right direction, I'm sure we can get this figured out. I just want her Jeep out of my hair...lol. Thanks guys.

1998 Cherokee Sport 4.0

FYI, when I jump start it, it runs great...pull the negative battery cable...dies immediately.

You're gonna need a multi-meter. Test the battery voltage with the Jeep off...should be 12.5 or so. Then test again with the Jeep running. Should be 13.5 or so if the alternator is working. Otherwise alternator is suspect.

A parasitic draw (something using power when the key is off) will drain the battery, but once the Jeep starts that parasitic draw no longer has an effect. The fact that your battery is drawing down tells me that the alternator is not charging.

I had the mother-in-law pony up the cash for a new alternator and it seems to be charging now....which is stellar because I was leaning towards the PCM regulating the voltage improperly. Lets just say, it's back on the road and the alternator is for sure charging now. So I think we're golden...Thanks man!!