I would imagine that, if you've ever answered "No" to the cookie question, then you wouldn't see the "remember me" box. That's what's going to set the cookie and it would be superfluous under those circumstances.
I answered "Yes" to the cookie question initially and have never been asked again. If you similarly only get one shot at it when you answer "No", perhaps that's what's causing the odd problems people report. (What happens if someone want to change her/his mind?)
– logging in under another user name will cause a "forget me" and demand a re-login
– logging in from another computer (even from the same IP) will cause a "forget me" and re-login
– when cookies are accepted and the "remember me" is working correctly, shutting down the computer at night (or any other time) has no effect on it.
Edited By Sid Herbage on 13/07/2012 01:38:58