I discovered that players who had been moved down on the pyramid due to the "inactivity" setting were not allowed to be challenged until they had first challenged someone else. Since there were a large group of players affected, none of them could challenge each other, so they were stuck in limbo. I had to delete and reset their logins (and turned off this feature).
Also, the top ranked player was moved down, because he had not challenged anyone (at the top level, he can't challenge anyone), even though he had been challenged and played others beneath him recently.