LAN... erm is messenger allowed to use in your lan on the first palce ...? a possible reason... would be that your network admin might be blocking your ports that you use to sign in to msn whenever you sign in and he notices it and blocks u...thus logging you out after some time....have you tried using other modified clients...? and if you use the computer which is in the lan for temporary purposes why not try using web based messengers until the problem is solved...
a good web messenger...
http://www.e-messenger.net/