Check Notification Settings
Settings > Notification Center > Mail > VIP >
Select Banners or Alerts
Turn on Badge App Icon
Make sure an Alert Sound is selected
Show in Notification Center is on (optional)
Show on Lock Screen if you want a notification when the device is sleeping.
Let me know if this helps.
Those all off. i tried to set my email on the computer to leave the messages on the surver and delete after 5 days, and it was getting the emails then, and keeping them, but it kept downloading the same messaes over and over on my computer so i turned that off and now its not getting anything or giving notifications at all. ugh