Password only filled after entering user name, do you have the same user name for two different passwords ?

otherwise try "sign in as a different user" to check it.

thank you

Thanks ideato for those suggestions. I have three different user names, so that's not it. I seem to have solved my problem inadvertently. In Gmail you can sign into one account, and then you can Add Account and sign in to the other accounts you have. This makes tabs of each account you sign into. Then you don't have to keep signing out and signing in. So I tried signing into an account where the username and password were remembered by Firefox. Then I added the problem account that Firefox was not remembering, and Firefox gave me the window to remember this account! I said YES REMEMBER THIS PASSWORD and it worked. I still don't know why it would not work when I signed into the account first and not as and Add Account. But I'm just happy it worked.

LornaLyons, thanks for sharing your solution for your problem with us, mark solve your reply to help others with the same problem.