I am having same issues here with my iPhone. The password disappears from my yahoo account setup. But only for one of my accounts. My second account has no issues. The same is happening on two of my computers. Both on IE and Firefox. The password is "forgotten" from my pc/iphone. Maybe something is erasing the cookie (cache file containing the pw) ? Dunno but this is really annoying now. May be with yahoo where the problem is. But is hard to get a hold of anyone there to even explain the problem.
I have changed my pw twice this morning because I thought someone had hacked my pw. But is hard to verify the new password since as soon as I login, the pw disappears forcing me to login again.
All this issues with yahoo today forced me to setup another account with gmail on my iphone. NO issues login on to it from iphone or pc.