In my limited testing the past day or so, it appears that the Facebook app must be open and running (in the background is okay) for the notifications to work properly. If you open the app and then open a bunch of other and it gets closed by the Android OS, the notifications will stop. Even if it is open and running, the notifications will not be instant. They come at 30 minute intervals at the very minimum. To test my theory, try opening The Facebook app and leave it running in the foreground for at least 30 minutes, then have someone send you an email on Facebook or something and see if you get a notification.