Did you disable notifications for Facebook? It seems like this is the case. To enable them manually, go to:
-Settings
-Scroll down (not to all the apps because Facebook is grouped with social media apps in the order of twitter, facebook, flickr and vimeo)
-tap facebook
-tap settings (within this)
-tap notifications and then put the slider to allow notifications
I have tried to explain this the best I can. If you are confused by the instructions, let me know and I'll include screenshots.