does this happen everytime the screensaver comes on?
that is strange. your msn should not sign out JUST because the "screensaveer comes on". --> make sure that your computer does not enter standby.
which operating system do you have? what options do you have enabled with the screensaver?
i am not sure how it works in windows 2000 if you have it. but in xp your programs should continue working in the background when the screensaver is running (even if you enabled the option to password protect your computer ie. 'on resume display login screen')
i believe (correct me if i'm wrong) that your interntet connection should be running UNLESS you
log off the user or you enter standby.
Edit: to me it completely sounds like your computer enters "standby"
Edit 2: you can disable that by following lp15's directions above (right click on desktop, go to screen-saver) and press on the power button on the right bottom corner of the display. there you have an option to disable your computer from entering standby.