After banging my head on this problem for a while and hearing what Chrysler/Jeep corporate had to say, I drove down to my local dealership on a snowy day. Luckily, there were zero customers in there and a bored (but very nice!) service tech had about an hour or so to sit and trouble shoot the problem with me. As it turns out, despite everything the corporate guys told me my software was WAAAAY out of date.
Then click yes to update the radio software. This update took me from 44.00.01 to 50.00.07. I specifically told the Chrysler/Jeep support techs what my software version was and they continued to tell me that there were no updates. Thanks a lot 1800iAmUseless email, chat, & phone support.
The big question… Is it fixed? Sort of. Yes, it’s updated but as soon as we tested it again after the update, the phone dropped off again. It took longer than the usual 27 seconds, but it still happened at the dealership. They don’t want to take any chances so they are going to swap out the head unit. That being said, it hasn’t dropped off once since then. I’m calling it fixed for now until it gets fixed again aka replaced.