Same on my sportage urban diesel...
Im from israel, we have another multimedia screen then in the US but it happens to me aswell.
Carplay can work for 20 minutes or so and then every 5/6 minutes it quickly disconnect and then reconnect.
Im using a genuine apple cable that i bought few days ago. (dont have wireless connection)
Also i went to the dealer to update the system software and still the same. (here we have to go to the dealer to update the software)
Still have my phone connected to the car bluetooth and haven't tired to remove it, maybe thats the problem..
But i also remmber that after i updated my phone to 16.2 it started to happend.