Are both sites showing a stream from the same Facebook Page? If so, that would be very strange.
The stream in the backend is always pulled on-demand. That means that it's not a cached version or something.. that's what JFBConnect sees from Facebook. As to why, that's a better question. Is there anything that's happening with the more recent posts, like are they set to private or not standard feed posts? Things like video posts or other non-text posts are not imported. That's about all I can think of, but I know that's not much to go on.
If you still need help, can you post (or Private Message) us:
* A url to the page with the stream
* A link to the Facebook Page
With that, we can at least compare what is shown on your site vs the missing posts to the Page.
Thanks,
Alex