1999 Jeep Cherokee needs a jump to start, and then dies when I take my foot off the gas. Has a rebuilt engine. Any ideas on what this could be?

First check the battery,if you have to jump it off,if battery is good,have the alternator checked,sound,s like it is cutting off for lack of power,meaning alternator not charging battery,or battery is bad.

Thanks. The battery was recently charged, and the car ran fine for several months after that. This problem began once the weather turned cold. I had AAA check the battery and was told that it had fully discharged

Personally, I would start at the basics.Fuel delivery, spark and air intake.See If your fuel filter is clogged or pump is starting to fail.A fuel filter is cheap to replace.If your charging system is not keeping the engine running, maybe the alternator or regulator.I think that has a built in regulator. How about the intake , is the filter clogged ? If these check out, I would have the crankshaft position sensor checked.And the distributor module. A diagnostic by a qualified mechanic can save you $$. Go to a reputable mechanic not the auto parts stores.They check engine lights, but they'll help you buy half the store without really solving your problem.Is the service engine light on ? Any code reads?

Thanks very much