The MOPAR trailer wiring kit that you buy from a dealer has the power for the relays that are part of both factory and dealer wiring connected to the 12 volt outlet on the dash that's always on. So long term the relays can drain your battery. The solution I and others used was to connect the wire to the fuse by the drivers door marked towing or something like that because it's switched
There's already a wire on that fuse and I soldered onto it behind the kick panel.
You can check by looking behind the dash outlet for a piggy backed spade connector that is specified in the instructions.
Now if your jeep has a EVIC then none of the above applies as the wiring is already in the right rear quarter panel for the towing harness
Here's a good rite up on the towing harness situation.
http://www.jeepkj.com/forum/showthread. ... tite+hitch
Also there was a F45 service bulletin for a flash to the body control module for something running down the battery.
BUT it could be the battery you have is just not up to a CRD's demands
