Usually error 66 is the other end of the connection closed the connection. So, whatever you are talking to may be closing the connection, not your LabVIEW program. If that is the case, then you will have to open a connection everytime.
If all of your commands are easy ASCII commands, you MAY be able to test this by using Hyperterminal. Set it up for Winsock and set the IP address and port. I sometimes have issues with Hyperterminal detecting a dropped connection. You can also use DOS's telnet application by going to a command prompt and typeing:
telnet <IP Address> <port>
This usually detects dropped connections pretty well.
I saw nothing in your VI which should cause the connection to drop.