I run two iPhones with ARC. One in my Pocket and one in my car. The one in my pocket works as expected, the one in my card did for some time and now shows: "Unauthorized" :-(
I’d first log out and back in on the affected phone, if you haven’t tried already. Next, try resyncing the car iPhone on your home WiFi. How regularly does this phone connect to your home network? If ARC goes several weeks without resyncing to the server, particularly if the server updates, then it will eventually expire its authorizations.
This state can also occur when that the ARC instance is associated with a non-existent unique server identifier. Have you migrated your RoonServer or restored a Backup since your last re-installed ARC on this iPhone?
The heavy-handed solution to this problem is to delete and re-install the app if none of the above is helpful.