The message from webhelp2 above is NOT Mozilla support.

Your ‘logged-in’ status is stored in special cookies. If the cookie is removed, you are logged out.

You may be in Private Browsing mode or told Firefox not to remember.

Type about:preferences#privacy<enter> in the address bar. The button next to History, select Use Custom Settings.

Turn off Always Use Private Browsing Mode Turn on Remember My Browsing And Download History At the bottom of the page, turn on Clear History When Firefox Closes. At the far right, press the Settings button. Turn on ONLY Cache and Form And Search History leaving the others off.

thanks for the instructions. My windows doesn't look like the one you reference. I did get the entry into the address bar, but then my window, doesn't seem to match your expected. Here is the top view at that point in my attach.

A post was flagged as Solved Problem. If the problem is not solved, please remove that flag. If you don’t, others that can help may not read this post.

Go to that message, and use the Undo link to its right.

My windows doesn't look like the one you reference.

The page you were looking is; about:preferences#home

My instructions said; about:preferences#privacy

We have seen more reports about not being able to stay logged in to ATT Yahoo mail for two weeks during the last few days (also reported on other forums), so it is quite possible that this isn't a Firefox issue but something on the Yahoo website and that they need to fix this.
You can consider to contact ATT for support.