After updating to iOS 5 or iOS 5.0.1, Yahoo! Mail seems to have a problem on the iPhone or other iDevice. Intermittently, the device will receive mail, only to have it not show up minutes later. The problem can be solved by following the steps below:
Step 1) After updating your device, sometimes you have to reenter your password in order for your mail to start working. To do this, go to Settings > Mail, Contacts, Calendars ? click on your Yahoo! account > Account > enter in your password where it asks for it. This should allow your email to be pushed to your iPhone.
Step 2) Set the mail app to show only the last 50 recent messages by going to Settings > Mail, Contacts, Calendar > Scroll down to Show > change to 50 Recent Messages. Restart phone by holding down the home button and the sleep/wake button at the same time.
Step 3) Delete the Yahoo! Account and then re-add it. Sometimes the settings and server information gets messed up when you restore from a backup.
Step 4) On the web interface for Yahoo! Mail, make a test folder and move the emails into this folder one-by-one. Sometimes there is one email that is causing the push to malfunction and once you find this email, the issue with push Yahoo! mail should be fixed.
Step 5) Go on to your Yahoo! mail with another computer, change your password, then log on and log off with the new password to make sure it works. Go back to your iPhone and change the settings to the new password.