I use an Apple PowerBook G4 at my apartment, connected to Time-Warner Cable; and an iMac G3 at home, connected with dial-up. (When I move back home, I’m definitely getting a cable modem!) Both machines are running OS-X Tiger.
On the PowerBook if I go to my Earthlink webmail page and log in, then navigate away from it, open another window and go to it, or go to it from an already-open window, I’m still logged in. On the iMac I need to log in again. Why is that? Has it something to do with the way I’m connected? Is it due to the different versions of Tiger? (Being on dial-up, I’m loth to download the many-megabyte upgrades onto the G3.) FWIW I also have to re-login on the PC at the office.