Facebook push notifications stopped

I have Facebook 1.5, which supports push notification for comments on my wall and chat. However, yesterday I went on Facebook's site and saw that someone had commented on something I had posted, but I had never received the push notification for that from the app! Then today, I was Facebook chatting with a friend on my computer, but my phone Facebook app was not notifying me as it had done faithfully since I updated my Facebook app.

Chat notifications don't come through unless I start the app and go into chat. After I exit, notifications go through until the chat ends. But they are supposed to come up without my starting the app.

I rebooted my Droid 2 to see if that would clear things up, but it obviously has not.

Please advise on how to fix this problem rather than suggesting alternative apps. I like the official Facebook app and would like to actually fix the problem.

Thank you.