Subject is a 2010 XK but solution may have general applicability:

Bluetooth had been working faithfully but failed to connect.
Cancelled the phone Bluetooth connection to the car but failed to reconnect.
Other items on the most network continued to function, so it wasn't a network problem.
Followed the XK Bluetooth flowchart, suspected BTM or antenna.
Removed and disassembled the BTM, sprayed thoroughly with contact cleaner. Dabbed dry with a clean towel.
Left in sun to bake while I ate lunch. Reassembled and re-installed.
Re-established BT connection, entering the random PIN offered by the vehicle.
All is well!
Works fine, lasts a long time!



PS: The XK is a convertible and I suspected water intrusion, although there were no sure signs.