Your messages.log looks like if it you use Neo4j Enterprise in HA / Cluster mode?
There are also exceptions that say that the client closed the connection without reading the full response stream?
What kind of client code do you have (stack, kind of interaction).
Caused by: java.io.IOException: Connection reset by peer
Are you writing to master only?
There are also a lot of other network issues in your log-file, perhaps your network config is not consistent.
e.g.
java.net.NoRouteToHostException: No route to host
Michael