An odd thing happened when I was looking through my contacts. I changed the sorting order (to Zone) and my radio vanished!
I checked all the tabs, changed the sort order back, visited the detective for the zone, closed/reopened the window, to no avail.
What did work was adding a new contact. My guess is that this forced a refresh of the list.
This may not be a reliable fix, though, so I'm reporting the bug in case it happens again, to me or anyone else.