This is a recurring issue and is widely discussed elsewhere too.
I havehad my iP5 for about a month and the FB sounds worked for about 2 weeks. After yet another FB update, sounds stopped working for FB notifications but I can't say the two events are linked. My email notification sounds also stopped (but I'm rather glad about that ... silent spam isn't a problem; it's a blessing!)
I think it's more likely to be an iOS6 problem.
Has Apple said anything about it anywhere? Links anyone?
Ok so apparently they FIXED it!!
-Go to the facebook app on phone
-Go to Account Settings
-Go to Notifications
-Go to Mobile Push
-Look at the top of the screen and it said "Sound for push notifications"
-Edit it to ON for all notifications
They fixed it I now receive sounds for notifications!!!!!
Tell people that are having this issue please