We had this problem with a SOA system written in Java. we were running both the client and the server on different machines and they worked fine for a long time, then those weird connection resets appeared in the client log and there was not anything strange in the server log. Restarting both client and server didn't solve the problem.
Finally, we discovered that the heap on the server side was rather full so we increased the memory available to the JVM: problem solved!