If you go to Settings>Apps>Mail>Accounts>Fetch New Data, what setting do you see under Fetch? Not all accounts will support Push notifications, so you need to have a Fetch setting. Manually will only retrieve and notify you of mail when you open the app. Automatically seems to only do a Fetch when the device is connected to wi-fi. I've seen multiple explanations of that, but have also read not to use it because of the fact that mail is not picked up much. The others for time work the best. My personal mail account is set for 15 minutes, so the mail is checked every 15 minutes and I'm notified if there is any new mail. Hope that helps.