I have had the same issue with my iPhone SE, since ios11. I have done a factory reset, then restored, and none of that lasted. My phone will disconnect from my car if I receive a text or email message, and that happens within seconds. If I try to make a call, it will disconnect from the car, but my phone is still making the call.
I've spent many hours on the phone with Apple, and most of them don't have a clue about anything they can't read, or any idea of trouble shooting outside of what their logs say. I guess you can't blame them for that, but they are of no help with this issue.
I am of the same mind as some others, and even though my hardware is all Apple, it's easier and cheaper to change phones than cars!