LightningZero, are you running on WiFi or 3G/LTE Data?

If it's 3G, then should be app problem. But for me, I receive most of the notification EXCEPT for group messages from the integrated People options and Messages (for any individual FB messages).

If you are using WiFi, there's currently a problem (which has been fixed, but we are only getting during February) where once you lock your screen, the WiFi is turned off after a few seconds. So it means most application will not work (or messages won't get push in the Toast Notification area)