Poppy & Heather, the site won't show you logged in 24/7. Once you've closed your browser or been inactive for 60mins the software is set to log you out. The reason why you are seeing yourself logged in constantly, is that each time you access the site your are logged in automatically, this gives the impression that you haven't been logged out (it's actually designed to do this). I can assure that as I type this you are not showing as being logged in.
Heather, if you delete cookies, it deletes all the cookies on your computer, when clearing cookies you should really clear temp. files too, this can get a little tedious, especially if you have a lot of websites you visit that require you to login as it'll clear that info too. Mozilla Firefox gives you an option to clear individual cookies only, but IE doesn't.