If the suggestions above don't help the situation I recommend using a password manager like Keepass or LastPass to create strong unique passwords for the sites you visit. You can also save notes like your secret questions and answers to the password entries. LastPass can automatically log you in to any web site you have stored in its database.
Answers & Comments
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I've checked the "Keep Me Signed In" box. Why am I still asked to sign in? - http://help.yahoo.com/kb/index?page=content&id=SLN...
What is Browser Autofill? - http://help.yahoo.com/kb/index?page=content&id=SLN...
Auto-fill troubleshooting - http://help.yahoo.com/kb/index?page=content&id=SLN...
If the suggestions above don't help the situation I recommend using a password manager like Keepass or LastPass to create strong unique passwords for the sites you visit. You can also save notes like your secret questions and answers to the password entries. LastPass can automatically log you in to any web site you have stored in its database.