Settings > Notifications, are they turned on at the top?
Settings > Mail, Contacts, Calendars > Fetch New Data > Advanced, Make sure it is turned on for the actuall account. Just because it is on for everything under Fetch New Data, does not mean it is on for that account. Also, Push is not available for every account type, so you may not be able to turn it on at this level (in which case you are out of luck).