Your ‘logged-in’ status is stored in special cookies. If the cookie is removed, you are logged out.

You may be in Private Browsing mode or told Firefox not to remember.

Type about:preferences#privacy<enter> in the address bar. The button next to History, select Use Custom Settings.

Turn off Always Use Private Browsing Mode Turn on Remember My Browsing And Download History At the bottom of the page, turn on Clear History When Firefox Closes. At the far right, press the Settings button. Turn on ONLY Cache and Form And Search History leaving the others off.

I closed Firefox yesterday evening, after making the changes suggested, above. This morning when I attempted to log in, I had the same 'Start from scratch' log in problem. I've included screen shots of the sequence of steps that I need to take every time I attempt to log in. (There should have been four screen shots, but the last one is not completing its download).

https://support.mozilla.org/en-US/kb/how-to-fix-preferences-wont-save

Note: Some software, like Advanced SystemCare with Surfing Protection, can protect files in the Firefox profile folder against changes. If you have such software then check the settings or uninstall this software.