IOS – Facebook push not working

For what it's worth, my iPod Touches' (2g and 3g) WiFi remains on when the screen is off, and I do get push notifications from various things (in fact, as I was typing this I got one from Ambiance). If you go out of range of known networks and "Ask to join networks" is turned on in the WiFi settings, you of course won't get push notifications unless you turn the screen on and accept an open network. The Apple battery life optimization page has a little more information, including how to control on a per-application basis what push notifications will work.

Just of note that Facebook is notorious for being extremely flakey when delivering notifications of any kind (whether they be system wide through the home screen icon, or even in-app). If you have Push enabled on both devices, the problems could lie within Facebook.

Also note that it may (read: should) be the case that when you check your account on one device, the notifications should disappear on the other, as they will be marked as read.

Additionally, it could be that Facebook's servers deliver a notification only once to any waiting device capable of handling them (remember they have millions of users to contend with). You'll have to contact Facebook to make certain of this however.

You can use mail to test it. If you send yourself an email, do you receive notifications on both devices? If you read the mail, do they disappear (get marked as read) on both devices?