So after changing my password for my Yahoo account, I am now consistently getting my e-mails pushed to my phone. It has been several days and usually by now the temporary fixes would no longer work. This seems to be a permanent fix.
Here are the steps recommended by Yahoo! which are part of this link (
http://help.yahoo.com/l/us/yahoo/mobile/topfaqs/iphone-02.html):
If there are problems, consider going through this process to make a clean password which can be the source of some problems:
1. Delete the Yahoo! ID on currently on your iPhone.
2. Turn off your iPhone.
3. Log into your PC and change your password. Many errors care caused by the way the iPhone encrypts some characters. Please ensure your new password has no special characters (any character which is not a letter or a number, such as @ or *). This will reset our registration systems and ensure that Apple treats your ID as a new connection.
4. Turn your iPhone back on.
5. Set up your Yahoo! account on your iPhone using the Yahoo! option. Please make sure that you enter your new password when setting up the account.
6. Make sure that your iPhone is not set to Manual Push. To verify this, please take the following steps:
1. Open Settings and Select Mail > Auto Check
2. Ensure that Auto Check is not set to Manual.
Those steps should trigger a re-sync between your Apple Device and our systems. Try mail again.