I'm short on time but wanted to reply as this might be of some use.
This happened to me recently. caused by corruption in sqlite file causes firefox to rebuild it and lose lots of cookie data (or it all).
Go into the firefox profile and you may see a few files like "cookies.sqlite" and "cookies.sqlite-rebuild" (or similiar, can't quite remember)
You may find that there is one of those files which is large in size, this is most likely the one which contains the cookies.
You can rename this to the proper filename of the current version, open firefox, and you should find the cookies are restored.
What I found tho was that every few days they'd keep corrupting themself and I had to keep going back and renaming the rebuilt file (or the large one) back to what it should be, and kicking out the faulty version.
Because I didn't want to lose all my cookies what I did was use some sqlite command line utility to run a repair on the database (file), then pull all the information out of it and push it into a new file, hoping in the process it wouldn't copy over any corrupt data which was causing this issue. Rename that file to what it should be "cookies.sqlite" and it's worked fine for several months since.
Zen 8000 Active