Had this problem today! My yahoo mail keeps on asking for password, I figured something's up.. I deleted all accounts on my iphones and ipad but when I tried adding them back, it says yahoo server unavailable..
But then i figured it out.. Just log in to your yahoo account on your computer, go to account info, manage apps and website connections, you'll see there the websites or applications that may have been suspended by yahoo because you changed your password.. Don't have to do anything.. I think that's the reason mainly.. So try adding yahoo on your iphone again, that should fix it..
Again, log in to yahoo from your computer, go to account info, click manage apps and website connections, that's it :)