Same thing is happening to me to
Is somthing wrong with hotmail site? or is it a virus/spyware which is doing it?
But I found out a way.
When u log on using MSN messenger,a window pops out saying there are new messages,click on that & it will take u to your inbox directly.
When manually loging in on the site it logs out on it's own.
This happened to me too a few days back, these days when you logout you see a new page asking you to logout completely or try again. If you dont logout completely you get this problem I guess. I didnt face this problem when I logged out completely & then tried checking my mail.