I'm not sure from a quick look. I just tested in IE8, Chrome, and Firefox, and I can see that the login button doesn't work when clicked. However, it's only on the page you linked to. If I go to your home page, the link worked in all browsers correctly. I don't know what's causing it, but on the realtyna pages, there's a Javascript error below regarding Mootools:
Error: el.set is not a function
Source File: http://homehotel.co.il/media/system/js/mootools.js
Line: 23
JFBConnect does not use Mootools on normal pages, but it does require Javascript to be functioning properly. If there's a JS error on the page, it can prevent our code from working, which appears to be what's happening hear. Have you recently enabled the new Mootools Upgrade plugin (in the 1.5.22 Joomla release), installed new components, or updated anything Javascript related? That's where I'd recommend looking. You may want to try disabling some features/components/modules on the site to narrow down what's causing the JS error above as well.
Finally, you're running 3.0.x of JFBConnect whereas 3.1 is out now. There are quite a few compatibility improvements (as well as other fixes) in the newer release that may help. However, nothing in this release would fix the problem, as the JS error is not coming from JFBConnect. Just wanted to alert you to the new release.
Please keep us posted on what you find!