If the phone shows signal when you wake it, that is the real signal. And if there is signal on the phone it is working fine and will receive calls.
It sounds like there is a bug in updating the car via Bluetooth. As Windows 8.1 is older and will not be receiving any updates, I suggest you try Windows 10 on your phone (one first!).
Upgrade Advisor app for Windows 10 Mobile - Windows Help
The other nice thing about Windows 10 is that it contains a Feedback tool to report issues, which then often get fixed through updates.