Go to your preferences panel > General Options > Miscellaneous.
Under automatically change my status after a period of inactivity, Make it checked, Delay 1 Min, Status: Appear Offline.
Open A Window with someone and wait a minute, It closes the window.
I think this happens too with any delay setting.
In Messenger, Tools > Options > Turn me to away after a period of incactivity is unchecked
Windows Version: Windows XP, 5.01.2600
Messenger Client Version: 6.2.0137
Messenger Plus! Version: 3.01.0094
I know if you choose appear offline from the messenger window, it will ask you to close all windows. And I know that in a conversation, /appearoffline only makes the window grey. But when you leave it, it just closes.