I have this problem as well. Iphone 6S plus with the latest 10.2.1. My vehicle is a BMW.
My Iphone will connect to my BMW 328I bBluetoothfine however when a phone call comes in i can answer, but I cant hear them and they cant hear me. The phone, after 5-6 seconds will disconnect and then become unpaired with my BMW. Once I re-pair I can make / recieve one (1) phone call, and after that call is completed, the process will repeat itself again of disconnecting when answered if another call comes in.
With IOS 9, I had ZERO bluetooth related problems. Seriously, zero issue. Then something happened. Since upgrading to IOS 10 I've had nothing but Bluetooth issues between this phone and my automobile. So what happened? Well I know my car didn't change, but my phones operating system sure did. Something happened that caused a perfectly good Bluetooth connection in IOS9 to stop working well in IOS 10. I have the latest firmware that BMW supplies for my year / model of car, and I am upgraded to the latest version IOS that Apple offers.
I don't need finger pointing as to who is to blame. Since I've see many other BMW owners as well as other vehicle owners having difficulties as well, I would be very on point to say this is in Apple's court to fix. Android connects reliably. Apple does not. This will be a factor when I upgrade my phone very soon.