Thomas,
Thanks for the link to your page. Still not sure why the Like buttons would disappear, but Facebook doesn't like multiple extensions trying to communicate with it. The way communication takes place is through Javascript loaded by a file called "all.js".
Without JFBConnect installed on your site (right now), I'm seeing:
* The all.js file loaded 3 different times
* Additionally, the FB.init call, which is what initializes the Facebook API with certain configurations is called twice
If you load JFBConnect again, you'd have 4 inclusions of all.js and another FB.init call. These all slow things down, and cause extra conflicts. To use JFBConnect, the first thing we'd recommend is disabling all Facebook integration from other extensions, at least initially to test. Then, start re-enabling other features as necessary to narrow down when things break, and let us know. We'll help you figure out how to get things working with both extensions, or how to get JFBConnect to do what you're looking for.
Thanks, and good luck,
Alex