Make sure you have not disabled the password management feature in Firefox Settings. Click the Firefox menu button -> Settings -> Privacy & Security and go down to the Logins and Passwords section. The Ask to save logins and passwords for websites setting must be check-marked.

For more information see Password Manager - Remember, delete and edit logins and passwords in Firefox

... and if the above doesn't help, see Usernames and passwords are not saved.

Can you use "Create New Login" ?

• https://support.mozilla.org/en-US/kb/add-login-firefox-password-manager

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