My best guess is that you have the System - Cache plugin enabled and it's ordered before (lower number) than the JFBCSystem plugin. The System - Cache plugin should be last (highest numbered) system plugin so that it's caching the page after all the other system plugins have done their work.
If that doesn't help, let us know and we'll help how we can. I just viewed your home page, and the Like button was properly showing, so I couldn't see the issue.
Thanks,
Alex