Dominik,
That obviously shouldn't be happening. There's a few issues I can see with your page. First, it seems like you're using the Joomla System - Cache plugin. If so, that should be ordered last (highest numbering). If it's ordered earlier than other System Plugins, they won't function when the cached version of the page is loaded, and that's a problem with many extensions, including JFBConnect and JLinked.
Fixing that likely won't help the problem, but it may. If not, can you let us know what you're using for SEF URLs, Joomla core SEF or a 3rd party extension? Also, let us know if you're using any minifiers or other optimization type extensions. The jlinked.css file should include the full domain and path to the file on your server. On your site, it's looking to be just a relative link, and I'm not sure why that's happening unless some other extension is modifying that URL.
Hope that helps get you started.
Thanks,
Alex