The only reason that comes to mind that this might happen would be if all the new post are awaiting moderation and have not been approved. Under these circumstances the count will not decrement on simply reading the post. Is this likely or possible?

Well that’s how it works. The admin (specifically) is given a queued list of the most recent posts. It is the admin who needs to check them. If you don’t want to check them you can remove the queue on the very front page of the forum in the new post list at the bottom. On the title bar above the new posts is a delete button. This removes the queued list - except for any that require approval.