so i tried as well same issue as with explorer,
i just installed opera a year ago,
and made it remember the login.
now i only get a log out after several hours.
this was in explorer and FF after a few minutes,
considering the length of some of my posts,
you will imagine how disturbing that was for me.
by coincident i tried opera and since then the problem is gone,
you do need to set and tell it to keep the login remembered.
there are versions for on a usb stick,
you might try that first before installing a full version.
i never ever used IE and FF anymore since then.