The problem is that united.com has a third state, where it looks like you're logged in (no "sign in" button), but you're only sorta-kinda logged in for some purposes but not others. And there's no real indication of this, other than fare codes not showing up or award availabity being limited (which is of course less obvious). And since there's no "sign in" button, there's no way to quickly fix it; you have to go find a screen that would require full login (like your account, or viewing the details of a reservation), and then back to what you were doing.

The only answer I've found is to NOT check "remember me"; that seems to make auto-logoff really log you off, which ironically means it's easier to log in again.