Hi,
I've just had the exact same issue in my new VW Tiguan, started happening on day 3 of ownership. Just done some searches and it seems it is not uncommon and occurs on lots of different cars, with no clear solution offered. Some even have open tickets with Apple to try and to identify the issue.
Some suggest it is a poor lightning cable connection causing intermittent connection / disconnection but I'm not buying that. You would know this surely when charging the phone.
One post suggests that Car Play will always try and take priority over the cars selected mode if it is the first connection made upon starting up. Therefore, at the end of a journey, disconnect your phone first and put your car into radio mode. When you get back into your car, start up with the car still in radio mode 'then' connect your phone, at the end of the sequence. The poster suggests this will prioritise your cars system over Car Play. Car Play will still work when called upon but will not keep assuming priority.
This is just some advice I have seen with my searches and I'm yet to try it. Really hoping it works because the idea that Car Play and the car audio system are incompatible is quite ridiculous.
Fingers crossed.