lammert - 10:03 am on Jun 3, 2010 (gmt 0)
In your configuration, Courier is listening to the IMAP port 143 for requests of Squirrelmail or other IMAP clients. If that connection gets dropped, there may be an authentication problem in Courier. Reading your configuration files it seems that all the user and password information for the Courier accounts is stored in a MySQL database. The first thing you should therefore check is if that user table has been uploaded correctly in MySQL.
Another thing not directly related with your question but nevertheless important is that you may want to check the services which are currently accessible from the outside world. Almost all services in your netstat list can be accessed from the whole Internet. Some services like for example telnet, imap2 and pop3 should either have only local access, or should be switched off completely because you have already running encrypted versions of them as ssh, imaps and pop3s. Running encrypted versions of these services has no security value if at the same time unencrypted access is also allowed.