I'm continually hearing more and more from users who can't stay logged in.
Have you tried the below? I think I got the advice here. This is the advice that I give to my users and it works for their issues.
In IE, go to:
Tools / Internet Options / Security / Trusted sites / Sites
Deselect the "Require server verification" check box
Add yourdoman to the zone:
http://www.yourdomain.com/