This issue showed up in the master logs as "ERROR: unable to get tablet server status". The tservers appeared to lose connection for a brief time, less than 30 seconds, but then start communicating again. The server would then show up by IP in the list of Unresponsive servers and by hostname in the Tablet Servers when looking at the Tablet Server page of the monitor.
I can verify applying this one line fix to the 1.4.4 tag removes the server from the list of unresponsive servers and balancing begins again when there are no unresponsive servers.
The "unable to get server status" should still show up in the master logs. Maybe it is actually meaningful.