If it's any help, I'm currently on my work PC. In IE9, if I log in with "remember me" set, close the browser and re-open, I'm logged out. If I do the same in Firefox, I'm still logged in.
Previously, I cleared the cookies in Firefox, and attempted to do it in IE using the F12 menu, but it doesn't seem to be playing.
Looking at the cookies in IE using the F12 menu, I've got multiple instances of the cookie set, with a variety of expiry dates:
Cookie Information -
http://www.tehforum.co.uk/forum/lpost.php?webtag=DEFAULT&replyto=40507.8
NAME forum_style
VALUE tehforum
DOMAIN www.tehforum.co.uk
PATH /forum/
EXPIRES 12/10/2013 16:53:48
NAME user_logon
VALUE wingnutkj
DOMAIN www.tehforum.co.uk
PATH /forum/
EXPIRES 12/10/2013 15:25:28
NAME user_token
VALUE a token
DOMAIN www.tehforum.co.uk
PATH /forum/
EXPIRES 12/10/2013 15:25:28
NAME forum_style
VALUE tehforum
DOMAIN www.tehforum.co.uk
PATH /forum
EXPIRES 24/08/2013 12:44:26
NAME user_logon
VALUE wingnutkj
DOMAIN www.tehforum.co.uk
PATH /forum
EXPIRES 24/08/2013 12:44:26
NAME user_token
VALUE the same token
DOMAIN www.tehforum.co.uk
PATH /forum
EXPIRES 24/08/2013 12:44:26
NAME forum_style
VALUE tehforum
DOMAIN www.tehforum.co.uk
PATH /
EXPIRES 27/12/2013 19:41:23
NAME user_logon
VALUE wingnutkj
DOMAIN www.tehforum.co.uk
PATH /
EXPIRES 04/06/2014 14:11:52
NAME user_token
VALUE a different token
DOMAIN www.tehforum.co.uk
PATH /
EXPIRES 04/06/2014 14:11:52
NAME sess_hash
VALUE a hash
DOMAIN tehforum.co.uk
PATH /
EXPIRES At the end of the Session
Any use to you?