I had a lot of problems with Carplay in my car. Got a loaner, totally different car, also a lot of connection problems. It was worse then my own car. Turned out that it was the cable I was using, which was not from Apple itself (but was MFi). Now with an official Apple Lightning cable 0 connection problems. Works every time, don’t have to fight anymore.
Sooooooooo… is it your cable?
Yeah I also doubt that when that is the case