I had exactly the same problem twice now. I was able to solve it by removing one or two fuses (in the cockpit, not in the engine area), plugging them in again, close the vehicle with the key, reopen and retry. I should have the problem a third time to determine exactly which fuse it is :-)
A small disadvantage is that I also had to reset the time and the counters (average consumption and the like) were reset to 0.
I did not have to re-pair my phone. Luckily, because that lasted over half an hour last time before it had taken over all my contact data.
I have an old smartphone with Windows Mobile 6 and my wife has a simple Nokia, so it has nothing to do with your iPhone.
Next time I think I will first try to localize the bluetooth module under the driver's seat and unplug that. I suppose it's that one which gets stuck and is reset by unplugging the fuse.