Did you check the "Clear history when Firefox closes" settings?

If clearing cookies didn't help then It is possible that the cookies.sqlite file in the Firefox profile folder that stores the cookies got corrupted.

• rename/remove cookies.sqlite (cookies.sqlite.old) and if present delete cookies.sqlite-shm and cookies.sqlite-wal in the Firefox profile folder with Firefox closed in case cookies.sqlite got corrupted.

You can use the button on the "Help -> Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page.

• Help -> Troubleshooting Information -> Profile Directory:
  Windows: Show Folder; Linux: Open Directory; Mac: Show in Finder
• http://kb.mozillazine.org/Profile_folder_-_Firefox

Ty @cor-el for your help !

They made a new update to solve the issue.

The Nightly devlopment channel meant more for Testers and Devs is not meant to be used like a stable version. As you may know it gets checkins with two updates each day and as a result this can often lead to issue(s) until fixed, finished or reverted.

A place you can follow and discuss the Nightly builds updates is in http://forums.mozillazine.org/viewforum.php?f=23 though Josa is on break until Friday.