Constantly entering account and password info

I'm just a new hotmail user and can't find out how to avoid having to reenter account name and password every time I go back to my mail. With Livemail I only had to sign in when at a new computer, but even if I move from an incoming message to a site referenced in the message it seems like I have to reopen Hotmail. And clicking the little icon that offers to "keep me signed in" just doesn't do anything!

Has anyone figured this on out?

Thanks