Not Receiving my Email Push Notification Alerts

My iPhone5 always used to make a bell sound when someone would send me an email, whether or not my phone was sleeping or being used at the time.

Now for some reason, the bell only rings when I physically open my email icon and check to see if there have been any messages received.

I went into settings and it says the Push notification is on and the sound is activated, but yet it doesn't seem to work for some reason.

I am confused as I do not know what would changed to make it not work anymore.

Can anyone help me?

Thank you very much!