Not what you want to hear, but Yahoo has been hacked several times recently, and I suspect this is part of the stable-door-closing.
If you have to use a webmail-type service, the best bet is to switch to Gmail: so far, that's worked well.
Better is to buy your own domain (under £5 a year in the UK), set up mail using your domain address, forwarding to wherever your ISP's POP or IMAP mailboxes are. Once you've done that, changing your ISP or provider becomes transparent to your contacts.