I have experienced great difficulty with my new Android Moto X syncing with my Tesla S. My old BlackBerry never had this problem, and my Moto X doesn't have this problem with Lexus cars. The problem is two-fold. First, the blue tooth "disconnects" by itself in the middle of a call, and then it may, or may not, "reconnect" by itself. So it's like a dropped call, except that the phone is still connected. Second, once the phone is "paired" with the Tesla S, it does update all contacts in the phone and recent calls, etc., but only to the date of the pairing. The Tesla S does not pick up any recent calls or contact changes in the phone after the moment of pairing.
Noooooo! I sincincerly hope that its a fluke, as that will most likely be my next phone. Have you tried the forget device/reboot screen/pair device method. If that doesnt work, id go back to the carrier and have them test it with one of their phones to see if the problem is isolated to the phone.
I had a Galaxy Nexus, and the bluetooth was pretty terrible. When I got the droid x it was fixed and everything worked as expected. My thought is that its likely the phone and not the vehicle.
I had the same problem with my Moto X. It seems rebooting the system (holding down both scrollwheels on the steering wheel), solved it...