Connection to Server Lost when loading some existing worlds

After selecting an old world file (I had been playing it in 14w27b), the world loads and begins to render, then a message reading "connection lost" and "server closed" appear and then the crash report screen appears.

Creating a new world did not cause this problem. Loading some previous worlds also worked. I was able to reproduce it with worlds I had opened using 14w27b. These worlds also had some redstone clocks ticking.