For those that need a more detailed explanation between "push" and "fetch", it is below. For those of you who know all about this and don't want more "not helpful" information, please ignore.
Yahoo mail supported "Push" which means that when an email message for you reached the Yahoo server, it was forwarded to your personal email account and at the same time "pushed" to the Yahoo email account on your Iphone. In my case that last process used to be so fast that I received messages on my Iphone before I saw them in my inbox on my computer.
With"fetch", the Yahoo email server does not automatically push messages to your Iphone. Instead, the Apple Iphone process, on a particular schedule (15 minutes, 30 minutes, or hourly) goes to the Yahoo server and fetches all of the "new" messages since it last fetched and sends them to your Iphone. Receiving them on your Iphone is exactly the same as Push in the way the message looks and what you hear. If you have set your phone to give you a beep or some sound notification when you get new mail, you will get that with both the push and fetch process.
In fact, fetch is the way Gmail works. Gmail does not support Push.
So, if you set your yahoo account to fetch messages every 15 minutes, you are not getting them instantly like you do with push, but you are still getting them on a relatively timely basis. And you will know when they come.
To make the change from push to fetch: in Settings, go to Mail, Contacts, Calendars. Under all of your email acounts there is a Fetch tab. Go to this and on the next page do the following: Set Push to Off. Then set Fetch to the schedule you want. Then click "Advanced". And on the next page you will see your Yahoo account and set it to Fetch.
The only problem with this is that if Push starts working again, you won't be able to tell on your Iphone. You will either have to read it on this Board, someone is bound to let us know. Or you can change your Yahoo account back to Push every once in a while, and see if it works.