I was having some CarPlay connection issues, but it turns out that I was getting a pesky iTunes "verify password" alert on the phone, and it was breaking CarPlay's connection. I have been running with BT paired and usually plugging in to CarPlay, and haven't had any more drops. I was going to unpair my phone because it takes a second for it to switch over from BT to CarPlay.Correct, I was referring to having a single iPhone connected to both simultaneously. I have found that connecting my iPhone to just Bluetooth works fine & connecting via a cable w/ Bluetooth disabled on my iPhone or the iPhone is not paired also works fine. But when your iPhone is paired and actively connected to the cars Bluetooth and you have the iPhone connected to the front USB port (on my car) at the same time - problems occur.
It may also depend on your phone. The phone drives 90% of the CarPlay interface via a sort of external display. I have an 8 Plus FWIW, older phones may be a little less performant (my 6S was).