Not too sure on losing network coverage whilst in the car - can't see any reason why that would happen unless you are in a low signal area.
The profiles I mean are almost like permissions that the bluetooth has for each device i.e. can it do audio, calls, data etc. You can find this by going to the bluetooth settings menu and looking at the settings for the device you are trying to connect with.
Probably still worth trying another phone if you can.
As per the PM I sent you, I'm wondering if you're missing the sim card from Audi connect and that could be giving you problems?