The Android Facebook app is and always has been dodgy with notifications in my experience.
They seem to work when it feels like it. I have had this experience on all of my phones. My wife is the same with her Desire S.
Previous Phones: HTC Google G1, HTC Hero, Nexus One, Nexus S, HTC Desire HD, Samsung Galaxy SII, HTC Sensation, Galaxy Nexus, HTC One X, Nexus 4, HTC One
Previous Tablets: Motorola Xoom, Nexus 7.
Current: Nexus 5, Sony Tablet Z LTE.