Just to make sure:

Type about:preferences#security<enter> in the address bar. Look under Logins,

Note: For Firefox v56+ its; about:preferences#privacy Look under Forms & Passwords +++++++++++++++++++++++++++++++ Turn on Remember Logins. To check the passwords you have listed, press Saved Logins.

Press the Exceptions button and see what's inside.

A detail like a website remembering you (log you in automatically) is stored in a cookie.

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

• you can create an Allow exception to keep specific cookies, especially in case of secure websites and when cookies expire when Firefox is closed.
• Options/Preferences -> Privacy & Security
  Cookies and Site Data: Exceptions

In case you use "Clear history when Firefox closes" or otherwise clear history.

• do not clear the Cookies
• do not clear the Site Preferences

• Options/Preferences -> Privacy & Security
  Firefox will: "Use custom settings for history":
  [X] "Clear history when Firefox closes" -> Settings
• https://support.mozilla.org/en-US/kb/delete-browsing-search-download-history-firefox

• clearing "Site Preferences" clears exceptions for cookies, images, pop-up windows, and software installation and exception for password and other website specific data
• clearing "Cookies" will remove all selected cookies including cookies with an Allow exception you may want to keep

Both our replies are marked unhelpful.

Does the remember feature work on this forum?

This is cookie related like I posted above. If you do not keep cookies from these specific website then you will have to login again with every visit.

Make sure you do not run Firefox in permanent Private Browsing mode (Always use Private Browsing mode; Never Remember History).

• https://support.mozilla.org/en-US/kb/private-browsing-use-firefox-without-history

• Options/Preferences -> Privacy & Security
  Firefox will: "Use custom settings for history"
• remove checkmark: [ ] "Always use Private Browsing mode"