Don't know if this will work for everyone, but it seems to have sorted out my Evo 3D no longer receiving posts after the ICS update from Sprint. Little back history: I am a former BlackBerry user, and had the app an notifications setup on my BB. When I switched to Android, everything worked fine, until HTC and Sprint finally got the ICS update rolled out to my phone a couple days ago. Then, suddenly, no more notifications. I tried clearing the data and uninstalling/reinstalling the app, but still no updates. Then I checked in the All Apps list (not just the downloads) and did the steps below. My notifications have been working just fine since.
Go to:
Settings -> Apps -> All
Scroll down to the Facebook listings (mine had 4 total).
Tap each listing (except the one that only says Facebook and has the regular Facebook logo) and disable them. I disabled 2 Facebook Chats and the HTC Facebook.
After doing this, my notifications have been coming through normally. So, may be a conflict between these apps.
***Update***
As a note, I re-enabled the apps after a few hours, just to see what would happen. Notifications are still coming through normally (and it's been a few days since I turned them back on). So, if you use these apps (such as the HTC Facebook integration for being able to actually specify which folder you want photos you share to upload), it seems ok to turn them back on.