CarPlay keeps disconnecting, is my cheap cable the problem?

if a good cable doesn't fix it, go to Settings > General > CarPlay on the phone, forget the car, and pair it again. also try the car's other usb ports, in a lot of cars only one of them actually does CarPlay and the rest are charge only.

Very likely. Cheap cables are the top cause of CarPlay dropping. Try an Apple or MFi-certified one first, and while you're at it pick the lint out of the phone's port with a wooden toothpick - that also causes drops.