The issue with the Roundcube setup you have is also giving me issues, so it has to do with the setup you have on your server as well. One thing I noticed is that you have it running in an IFRAME (probably due to the CMS you use).
Roundcube is not designed for this and I suspect that is causing all of your issues. Firefox has security settings to disallow cross-site loading I believe, and that could greatly hinder the javascript performance of Roundcube. I would recommend having E-Mail open up full screen (might require modding your CMS).