First, make sure Notifications are still on under Settings > Notifications.
If you are still unable to receive notifications and you are using a Wi-Fi connection, verify that the network or firewall is not blocking access to port 5223.
And if that doesn't resolve the issue, try resetting the device:
Resetting your device
Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears.