I also lost Bluetooth capability after upgradeing to iOS6 on the mobile-ease hands-free communication system in my Ford vehicle. This is on an iPhone 4s. Everything worked fine for over a year before I upgraded to iOS6. The iPhone pairs fine (I tried deleting the pairing and repairing, but didn't help) but when I receive a call, the iPhone only vibrates (I am not in vibrate or silent mode), the hands-free system does not ring and cannot answer the call using the hands-free system. I can still answer the call if I use the iPhone. If I try to place a call using the hands-free system, I don't hear the answer on the hands-free system but the call does appear to go through as the recipients tell me their phone rang twice and then it disconnected.
Now if I want to communicate using my phone while in the car, I will have to break state laws that only permit hands-free operation of a cell phone, even not considering the safety issues involved. This is inexcusable and needs to be resolved. I also don't understand how something like this was never found during beta testing.