I would like to share with everyone my solution to this problem, as I had been experiencing the exact same issue for the last few months. I have read through this entire thread and through everyone's comments. The following steps are guranteed to fix your problem:
1) Delete your current yahoo mail account on your iphone
settings
2) Sign into your yahoo mail account from any computer (mail.yahoo.com)
Once signed in, go up to the top right corner and place the mouse icon over your name (in between the settings and the home icons,) and a window will pop up. Click on 'Account Info.'
- On the top left corner, click the 'Account Security' icon
- At the top, if you have your Yahoo Account Key enabled, YOU MUST DISABLE THE YAHOO ACCOUNT KEY
- After disabling the Account Key, you will see multiple previously hidden options open up on the Account Security page. At the very bottom of the page, enable the option that says 'Allow Apps That Use Less Secure Sign In.' (Leave this page up, as you will need to come back to it for the last step)
3) Create a new yahoo mail account on your phone
settings
- accounts & passwords
- add account
- yahoo (follow the step by step instructions)
4) Your yahoo mail should now be working normally through your apple mail app on your iphone, however I would send a test email to yourself just to make sure
5) Finally, go back to your computer to the Yahoo Account Security page that you previously left open, and this time, DISABLE the option that says 'Allow Apps That Use Less Secure Sign In.'
If done correctly, these steps will fix the problem, while not compromising your security. The biggest issue is the Yahoo Account Key.