Unfortunately your going to have to find what is draining it, and it might be trial and error here.
Have you added anything? GPS, Stereo or Amp, CB, anything?? If you have anything plugged in or wired in that isn't stock suspect that first, no matter how new it is, etc.. Sometimes it's the simplest crap that gets you.
If there is nothing to suspect go out after its dark and make sure no interior lights are on or such. I had this problem on my minivan, the kids would turn on these back reading lights and they were not noticeable during the day, but at night i caught site of one being on and that explained my weak battery some mornings.
The front and rear interior lights, the front map lights and the rear cargo light, can be turned on manually by pushing on it, so maybe something got turned on by accident. Also if you have lighted vanity mirrors flip down your visors and open and close them a few times and make sure they are turning off, easier to tell at night because you would see light around the edge of the door if they were on while closed. Sometimes the switch goes to heck in them, or it just gets sticky and intermittent inside, seen it before!
Also in the dark at night just make sure nothing else is on that shouldn't be!
And last but not least if none of that helps pop the hood and disconnect the negative battery cable and let it sit overnight, then in the morning reconnect the cable and see if it still starts. If it does then the battery is fine but you still have something drawing too much power while off.
If it comes down to that the only way is a fuse at a time. I would pull the fuse for the radio first, i have seen some posts on other forums about chrysler radios going bad and pulling an amp or more in standby.
The thing is if your battery is in PERFECT shape it takes a long time to drain it with an amp or less. You said from 10pm to 5:30am, thats on 7.5 hours, an average car battery has a capacity around 40-50 amp hours. That means if you had a perfect capacity of say 45 amp hours you should be able to draw a 1 amp load for 45 hours, yeah i know guys this isn't perfect math as there is a lot of variables, temp, battery age, wire voltage/current drop, etc etc...
But lets just say if you have a 2 amp draw on that battery when the engine is off you should be able to let that battery sit for 20+ hours before its too dead to start.
Another thing to check, when its too dead to start check the voltage at the battery with a voltmeter and see where your at. And if you know anyone with a digital meter that also measures amps then once the battery is topped off and starting fine shut off the engine and pull the positive lead off the battery and put the meter between it and the positive post of the battery to see how many amps are being drawn with everything off, should be less than an amp. I know even with all the added gear in my KJ i only see about 500-700 milliamps of standby current being drawn, that's because usually my ipod is plugged in, cell phone, two-way radio gear that has keep alive power to its memory, etc.. But i never have a starting problem.