Detail like websites remembering you and log you in automatically is stored in cookies, so make sure you aren't clearing important cookies.

You can use these steps to make a website recognize and remember you.

• create a cookie allow exception with the proper protocol (https:// or http://) to make a website remember you

You can check that you aren't clearing important cookies.

• using "Delete cookies and site data when Firefox is closed" to clear cookies keeps cookies with an allow exception
  in 102+ version toggling this setting makes changes to the "Clear history when Firefox closes" settings and those settings prevail
• using "Clear history when Firefox closes" in Firefox 102+ honors exceptions and keeps cookies with an allow exception, previous versions removed all cookies

Make sure to keep the "Site settings".

• clearing "Site settings" clears exceptions for cookies, images, pop-up windows, and software installation and exceptions for passwords and other website specific data

• Settings -> Privacy & Security
  Cookies and Site Data: "Manage Exceptions"
• Settings -> Privacy & Security
  Firefox will: "Use custom settings for history":
  [X] "Clear history when Firefox closes" -> Settings

If clearing cookies doesn't help, 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 when 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 -> More Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page (Root directory).

• Help -> More Troubleshooting Information -> Profile Folder/Directory:
  Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

In case this applies to you, there's a bug in Firefox version 110* that deletes all cookies when you only want to clear your cookies and other history for a specified time period (such as the last hour). This will be fixed in an upcoming Firefox version.

_{*Bug 1816279 Firefox 110 Forget the last x time deletes all cookies (see Bugzilla Etiquette before adding bug report comments)}

If you have selected "cookies" in your Clear History settings, remove cookies from the list of items to clear as a workaround. See Delete browsing, search and download history on Firefox for details.