I am a brand new user and for some reason, the information below posts (posted by, comments, tags, etc.) disappears for some unknown reason. It has happened to every post that has been added today (the first day).
It is a private family blog that for certain reasons (not you) I am uncomfortable unlocking to public viewing. I am certain that the info is ceasing to appear with time. I am not sure exactly when it happens, but at this point, it seems to occur when someone new posts. That is an assumption, mind you. The info is gone from below each post, though.
What theme are you using? The information with category, etc., below or above posts is called post metadata, and whether it shows or not on a post is theme dependent (some themes show it, some don’t).
Have you tried switching for a short period of time to another theme to see if it happens with the different theme?
Since your blog is private and we cannot see it then, you are most likely going to have to detail the problem out and contact staff about it: http://wordpress.com/contact-support/ (Mon-Fri 8am-4pm Pacific time) or using the “support” button in the upper right of your dashboard.