On my version, I have Firefox keep cookies until "I close Firefox" and I have this website's cookies in the Exception. It keeps the cookies with no problem. Also make sure you don't have Firefox removing the cookies in the "Clear Private Data". Check the same tab as the cookies tab, but a little lower, where it says "Private Data".
If you have "Always clear my private data when I close Firefox" checked, click on "Settings..." and see if the Cookies is also selected. If it is, the cookies will be removed every time you close Firefox, even if you add it to the "Exceptions...". It will be completely removed from the system and you won't probably see it anymore in "Exceptions...".
That is my experience with Firefox.
malu
