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A theme throughout what I was reading was that many who encountered the issue had upgraded from 6.5 to 7.6. My situation was a little different. I had not upgraded and had Director working for over a year without issue. It just stopped working all of a sudden.
I discovered the names of all my controllers were blank. In the forum I saw a suggestion about removing and re-adding controllers, I decided to just reboot my controllers one by one. In my environment, we had more than enough controllers to handle the load. Sure enough, rebooting the controllers ensured the names become populated again within Studio AND then Director started to work again.