I stopped relying on the iOS to push mail long ago and went with PushMail to rely on notifications. I would recommend a third party app because it's a lot more reliable and will provide you with a preview pop-up.
I tried all of the recommended ways to get mail to push via the iPhone's mail app including changing passwords to text only, deleting and re-setting up, I almost hired an exorcist. It was just to unreliable. I now have it set to fetch every hour but I know there's a new email instantly with PushMail's pop-up.