OK, under Tools > Options > Security > check "Remember passwords for sites".
Tools > Options > Privacy > check "Accept cookies from sites" > select "Until they expire"
Install CookieCuller: https://addons.mozilla.org/firefox/82/ Then choose which cookies you want to protect. Make sure you use CookieCuller to clear out your cookies, though... it only protects cookies if you use it to clear 'em. If you manually clear cookies through the browser, you just screwed the pooch.
Sounds like something outside of FF, then. I dunno if you have a cleaner of some sort (CCleaner, for instance) set to clean this stuff up, but that's what it sounds like.