With Firefox (24.4.0) if you visit a site with basic authentication you’ll get a popup asking for your username and password. When you’ve supplied it then Firefox will prompt ‘Would you like to remember the password for [site name]?’.
If you select the ‘never remember password’ option, then Firefox will add an exception at Preferences -> Security -> Passwords section -> Exceptions. You’ll be asked for the password every time you visit the site.
If you’d later like Firefox to remember the password, then you can remove the exception for your site and you’d be prompted whether to remember the password next time you visit the site during a new session.
However, it’s somehow possible for Firefox to never remember the password but also not store an exception, meaning Firefox will always ask for the password but never prompt to remember it and you can’t simply remove an exception to prevent this.
If this happens, do the following:
- Visit about:permissions (just type it in the location bar and hit return).
- Search for your site.
- Click the ‘Forget About This Site’ button.
Next time you load the site, Firefox should now ask you whether you want to remember the password.
Reference: How to save passwords after you’ve said “no” to the prompt, or add a password to password manager.