Jeep towed discharged when towing. This is new.

We've towed this Jeep for a few years now without any problems until this trip. We run the Falcon 2 tow bar and the braek buddy system. I followed the Jeep's owners manual, put the transfer case in Neutral, auto trans in park and switched the ignition key to the "ACC" position. We pulled into the campground yesterday after 570 miles and about 11 hours of driving to find the Jeep completely dead. I had a neighbor ask if I wanted a jump and accepted. Got it started after awhile and let it run about 30 minutes. Shut her down and checked a few times before I hit the rack and when I got up this morning. Started no problem. Figured it was operator error or just one of those things that happen on trips. I double checked everything before I left this morning, stopped after a few hours for a snack and it started right up again. Ok, fixed. Drove for another 400 miles or so, stopped for the night and it's dead. What gives? What do I check and how do I check it? I have a battery charger on her now provided by a nice fella in the campground, and I'm gonna charge it all night but need this fixed for my return trip to NJ next month.

Never had this type of problem before.

Thanks for any suggestions.

Bob