I'm having the same type of problem on a 2013 Journey SE with the Uconnect 4.3 radio. The Bluetooth module has failed on me twice in a few months and only a power reset by disconnecting the negative battery cable under the hood for a minute or two has cleared the problem both times.
I bought this vehicle used from a reputable dealer in June 2015 and had no trouble for the first few months. The Bluetooth Hands Free system is just a convenience to me, not a vital function, so if it goes out completely I can live without it. A good Bluetooth headset can provide the same function, with the exception of automatically muting the sound system. As for music streaming via Bluetooth, I don't use it. I prefer to hook up my 64gig iPod Touch to the USB port. It's more reliable and gets charged as well.
If the Bluetooth module does completely fail and I decide to replace it I'd rather do it myself, if it isn't a nightmare to replace. Why pay a labor fee if you don't have to? Does anyone here know where the module is located and how much work is involved in replacing it? Until then I may just keep a 15mm socket wrench in the rear storage compartment in case I choose to reset it while I'm away from home. Thanks to all who respond.