This week's book giveaway is in the OCMJEA forum. We're giving away four copies of OCM Java EE 6 Enterprise Architect Exam Guide and have Paul Allen & Joseph Bambara on-line! See this thread for details.
I would just keep one socket around. Sometimes when there is network congestion, an open socket pair will stay functional even when new socket pairs cannot be connected.
However, brief router outages can cause loss of connection, so even if you just use an open socket, you have to think about what to do if it goes down. Typically, you would just reopen the connection, and possibly resend any failed messages.