Are you connecting your phone to your car through the USB port or just just the phone by itself? If you use the USB port to charge and play through your radio, make certain you do not have lint stuck in the port. I carry my phone in my pants pocket and it picks up lint. I then occasionally have trouble charging or connecting to AirPlay in my car using a USB cable. Using compressed air and a wooden toothpick to loosen the lint and blow it out, I can clean out the port so everything works properly.
Hope these ideas help with the odd behavior of your iPhone!