Hello Clayton Kolb,
Welcome to Apple Support Communities!
We understand that you're unable to maintain a connection between your iPhone and your car stereo.
There are several factors that could impact the connection in your car. To isolate this behavior further, you can forget the car from your iPhone in Settings > General > CarPlay > [stereo name].
Then, on your car stereo, we'd recommend that you forget the iPhone as well. You can reference your stereo user guide for assistance.
You can also rename your iPhone in Settings > General > About > Name.
If you have any VPN software installed on your iPhone, we'd suggest that you temporarily remove it for testing purposes.
You can also use a shorter Apple approved Lightning cable to test with.
If you're still unable to maintain connection, we'd suggest that you reset Network Settings. You can go to Settings > General > Transfer or Reset [Device] > Reset > Reset Network Settings. This also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before.
If you're still experiencing the same behavior, we'd also suggest that you factory reset the vehicle stereo and test again.
If you need additional assistance, we'd recommend that you reach out to Apple Support directly here: Contact Apple.
We hope this helps.
Cheers!