Thanks. I've analyzed the logs and stats. In short, this exception was caused by a stop-the-world garbage collection from 03:19:39 to around 03:20:59 on the server. During this time the server was unresponsive. The server logs show client registrations and disconnects in quick succession at the end of this time period. These are a result of client's connection requests that were queued on the server side (by the OS) for the cache server process while it was unresponsive. When the cache server became responsive after the GC pause, it started to process those connection requests, but since the client had timed them out in the meantime, the server detected they were gone, and logged those "connection disconnect by EOF" messages. Then, the next attempt by the client to connect succeeded.
To avoid these errors stop-the-world garbage collections should be eliminated or reduced to a minimum. For this we recommend using the CMS garbage collector with GemFire cache servers (-XX:+UseConcMarkSweepGC). Also, we recommend setting Xms and Xmx to the same value, for optimal performance.