Somewhere here on Android Central a long time ago on what I think was the TBolt board someone posted a strange fix to this problem of not getting notifications. The fix was to find someone with a Blackberry device and log into your FB account from their phone. Apparently the association of a Blackberry onto your FB account set some permissions that fixed the push notifications across all the connectes devices.
Such a weird fix but alot of people reported success. I never could verify it myself because I was one of those that never had a problem. Then again I used FB on a Blackberry from my Storm days so my account has Blackberry associations.
FWIW my GN gets every notification every time. My FB widget also updates perfectly where my TBolt never did. Sometimes it took days for it to update on the TBolt.
The FB app seems to be very inconsistent across devices.