I did some research into where/how this was set. There is a configuration parameter that specifies how long a user's login is valid for from the time they first login. Right now it is set to the default of one hour.
So if you login to the board at 10AM, then go off and visit other sites (gasp!) and come back at 10:15, it would ask you to log-in again, even if you have the "Remember my login info" box checked.
I believe all the "Remember my login info" box does is remember your username so you don't have to type it in each time.