Dan,
Thanks for the access. Still not sure why it was happening, but the issue seems fixed now. Here's what we found:
1) When the {JFBCLogin} text was on the page twice, it worked.. This was tested by enabling your "Test" module with the text. When done, the Login With Facebook button would show up in the login area, but not the test area.
2) To get it to show up the first time properly, we re-ordered your System plugins. We move the JFBCSystem plugin to the last place, and things started to work. We moved it up one at a time and noticed it broke when it was before the RokZipper plugin. We'll investigate further why this is the cause, but for now, leave the JFBCSystem plugin ordered after that plugin.
Hope that helps, but if you run into anything else, let us know.
Thanks,
Alex