What type of connection are you trying to maintain? A shell login? file server connection? other?
If I remember rightly, a server connection is tied to a particular login. When that session logs out, all the processes associated with it, including the server mounts, are terminated.
Do you *really* mean you want the connection to stay open, or do you mean more that the connection should automatically re-establish the next time you log in.
There is a difference. if the connection really is open, then background tasks that run even when no user is logged in can continue to use it (e.g. Apache could serve data off a server volume when no user is logged in). To do this, though, the server mount has to be established by root during the system startup, not by a user once logged in. You'll need a startup item that calls the mount command to establish the server connection.
On the other hand, if you just want to re-establish connections when you log back in, that's pretty easy.
You should be able to use the keychain to save the password for future logins. This happens automatically if you use the 'Add password to Keychain' in the Options... dialog when you first connect.
Then drag the server volume's icon in your login Items preference pane.