What happens to the data for an app that gets removed during the update from iOS 5 to iOS 6?
The upgrade to iOS 6 doesn't remove apps, so this is more of a case where things don't go as planned so it's going to be very hard to discern why this happened in your case (and similarly for others with the same symptom but not necessarily the same cause).

You should not lose data from an app - iOS update or not and the procedure is the same as if you lost data on an app anytime. Restore the phone from your backup to get back the data.

In this case, you may (sadly) find that the backup has corrupted data (or data that is otherwise not usable), but in most cases, this cures the loss of data and will allow you to start moving forward on iOS 6.