I've seen some batteries fail in interesting ways.... i had one that worked intermittently. I figure it had a break in the main connection inside that fed the post. Give 'er a little tappy-tap-tap with a hammer, and it would work for a day or two..
I've also has a few with internal shorts.... the constant vibration and abuse evidently caused a couple of the plates inside to make contact. The internal resistance would cause it to drain slowly overnight. Put it on a charger, it would charge and test fine, but overnight, it'd be dead in the morning.
Bottom line, if your battery is not brand new, just swap it out, it's money well spent. Keep the old one around until you determine if that was the issue, if swapping the battery fixes it then the old one is junk, return it for your core.... if it does not fix the issue, it's one less thing you need to consider, plus you have a shiny new battery, and a spare that you can use for other things (get three of then, and I'll tell you how to build a portable DC stick welder.... well not THAT portable).
The other likely culprit here are the Jeep's battery cables. They are crap at best. The stock terminal clamps are an engineering travesty. Basically I see three potential issues with the cables. The battery clamps are crap (see above) and are not making good contact. Try to rotate each one by hand around the mounting post.... if you can move it, it's not tight and not making good contact. Try removing the negative one first, then the positive and clean them up, maybe polish the posts with some emery cloth, to see if you can get them cleaned up and clamping tight. Be careful to remove the negative first, so that you don't toast a perfectly good wrench/socket by shorting the positive against something.... That will scare the beejeebus right out of you and make a pretty spark show. On the bright side, you might just burn it to the ground and use the insurance money to buy another.... win-win.
The cables also have another end..... trace them from the battery to wherever they go... the negative one runs to a ground somewhere likely either on the frame or on the engine block (maybe both) check that each connection is tight. I cannot remember where the positive one goes.... sometimes directly to the starter, but on your jeep it might run to the TIPM (or maybe both).
Long post, I know, but lastly, the cables themselves can be broken internally, usually right at the end terminal points. Fatigue, vibration, work hardening, and thermal cycles can make the copper inside brittle, and it can break inside the insulation jacket. it may look fine from the outside, but it's knackered on the inside. Sometimes you can diagnose this by bending the wires a bit. it will bend much easier where the cable has failed. There is also sometimes a heat stain, or melted bit, as the cracked conductors can cause higher resistance and get hot.
Check the cables, swap the battery and report back. Also, any further detail on how it behaves might help....
Does anyone make quality replacement battery cables for these things? All of this reminds me of how much I hate the stock connections, and I have two new batteries setting on the workbench ready to go in. might be a good time to replace the stock cables/terminals.
Edit: I found these
Also a couple of handy diagrams that show where the battery wires go for the OP to check.: