It's nothing to do with your device, just the FB app. Once thing I did was go into my facebook via computer and turn all my notifications to send me an email. Then once I get the email, I check my FB. Certain times, my FB apps works all the time and certain times, it doesn't work.
Make sure your X has background data sync enabled...
Settings > Data Manager > Data Delivery > check all three (background data, data roaming, data enabled)
There's another category on the same screen Social Applications. I don't do those, but look in that and see if there's additional things to enable data sync. Make sure all appropriate options are checked.
For your email sync notifications, go to Settings > Accounts > Gmail (make sure there's a check by the three Syncs - Contacts, Gmail, Calendar. Then hit menu again and press "sync now." That should get you up and running, for the email at least. If you have other email accounts, check them and see if there are sync options similar to Gmail.
I use the paid version of Flow for notificaitons, the developer is constantly updating and making the app better and better so it was well worth the money. I still have the android FB app installed becuase I use Launcher Pro Plus and it uses the FB app (or mobile site but I prefer FB app interface) for feeds. The one thing about flow is that the widget does not show news feeds at aglance but rather will refresh, launch notification list, launch mobile site or laucn touch site.
Give Flow a try, it uses push notifcations using your emial and you can even set it to delte or archive FB email notificaitons so you dont clog up your inbox.