I think Yahoo was working out a new connection. Now on my iPhone mail, down under Accounts, it showed my 2 Yahoo accounts with the Yahoo logo and the same 2 accounts with no logo. The ones with the Yahoo logo have a different smtp than the old ones that were manually set up (using the smtp addresses supplied by Yahoo, BTW). I think they were making changes so that your iPhone can set up Yahoo accounts automatically and now the accounts were updated.. You know what I mean? Anyway, I went into the settings and saw the NEW ones showed "REQUIRED" under the password and needed to be entered. I put in my password, and it worked. I went to the original accounts and disabled them so that I didn't have the multiple inboxes with the same name, and all is working fine.
Check your settings again, and check frequently until that Yahoo logo one shows up, and check to see if THAT is the one needing password info. My original ones had the correct info, so that is why I couldn't figure out what the heck was going on. Please let me know if anyone else has seen this.