It sounds like the cookie(s) that sites set to prove that you already completed two-factor/multi-factor authentication got cleared. Were they just cleared once, or do you lose them every time you close Firefox?
Losing your cookies every time you close Firefox could be caused by modifying the History settings from "Remember History" to "Never remember history" or turning on "Delete cookies and site data when Firefox is closed" or "Clear history when Firefox closes".
Also, if you use the new Firefox icon with the mask to directly start a private window, that window won't save cookies to disk, so they won't be available in your next session.
If you can't find the cause of the problem, I suggest posting a new question on the Mozilla Support site. They have a team of support volunteers to troubleshoot malfunctions with your currently installed version of Firefox, while this site is focused on idea submissions for future versions of Firefox (looking ahead anywhere from 8 weeks to many months). Here's a link to the new question form (for Windows/Mac/Linux): https://mzl.la/3y1vQUQ
