Safari no longer saves password for certain websites!
For example, when I go to backblaze.com I can log in but safari won't even ask me to save the password. I went into the keychain and made sure there isn't already an entry in there.
Did they change something on that website? Try using /Applications/Utilities/Keychain Access.app and find the web site you are having problems with. Then delete that entry and run Keychain Accesse's First-Aid too.
Also go into Safari's Password Preference pane and delete the web site entry too. This way when you put your password on the affected site it should ask to save the entry again.