I've had two incidents where the car radio did not turn off after I got out of the car and set the alarm. In both cases, the radio immediately turned off when I opened the door again, but it had been on for more than an hour when it happened the first time. If it had happened when I'd parked for the night rather than during a brief stop while shopping, it could have easily killed the battery. Could be what's happening with yours.
FWIW, Jeep service found no issues when I had them check it out. Still, it's worth having them check the car over just to get the problem logged. If it keeps happening and they can't resolve it, getting it documented might be invaluable if you want to push for a lemon law buyback or a more expensive repair (if it happens again, I'm going to push them to replace the computer and the UConnect system).