Websites remembering you and automatically log you on is stored in a cookie.

• Create an allow cookie exception (Tools > Options > Privacy > Cookies: Exceptions) to keep such a cookie, especially for secure websites and if cookies expire when Firefox is closed.

Make sure that you do not run Firefox in Private Browsing mode.

• https://support.mozilla.com/kb/Private+Browsing

Do not use Clear Recent History to clear the "Cookies" and the "Site Preferences"

• https://support.mozilla.com/kb/Clear+Recent+History

Clearing "Site Preferences" clears all exceptions for cookies, images, pop-up windows, software installation, and passwords.

• http://kb.mozillazine.org/Cookies

Thanks for your fast response. I do "allow" cookies for the sites in questions and I don't use Private Browsing. I have just tried to sign on using my sister's email and password and it says: " The information you entered does not match our records. Please reenter your user ID and Password ". I also discovered that if I go to www.yahoo.com, I can log in to my sister's email. but still can't via www.att.my.yahoo.com. Although, I still can access it on Internet Explorer. Her email address is @yahoo.com whereas mine is @bellsouth.com. As you may know, AT&T joined with Yahoo for the email.

That issue can be caused by corrupted cookies.

• https://support.mozilla.org/kb/Cannot+log+in+to+websites

If clearing the cookies doesn't help then it is possible that the file cookies.sqlite that stores the cookies is corrupted.
Rename (or delete) cookies.sqlite (cookies.sqlite.old) and delete other present cookie files like cookies.sqlite-journal in the Firefox Profile Folder in case the file cookies.sqlite got corrupted.

• https://support.mozilla.org/kb/Cookies

Thank you so much, cor-el.....I didn't know about clearing history from the library for this particular site. I was totally lost, you're my hero!!!

thanks again, cozmos