I had a similar issue in the past and after some help it's now working fine for me. From what I know, there are two things you may want to look at:
(1) These two sites, http://www.fatsecret.com
are actually "different" addresses - you're login will be remembered differently for each of these addresses, so you might need to be consistent with the address you use.
(2) There are many browser toolbars, like Google and Yahoo and some antivirus type toolbars, that will automatically delete your cookies/sessions when you leave a site. So if you've got one of these toolbars you may want to take a look at your settings.
And then if all else fails you may want to try to delete your "cookies" in your browser and try again... not fun... but try and give it a shot.