Which flash version does the site use? If you installed the latest stable flash player for Linux it's probably version 7, but the newest version available (though not marked as "stable" yet, but it works great) is 9. You could try to update your flash and re-try; the package is at Adobe's site, but you can't for some reason find it directly (well I couldn't anyway). The easiest way is to open up google.com, search for "linux flash player 9 update" and pick up the Adobe's download site. There are two versions, "stand-alone player" is not what you want but the other one. Download and extract it, and inside the package there is a flasplayer.so file. Copy that file to your Firefox' plugin directory and restart your browser (warning: the file is named exactly like version 7 plugin is, so if you don't want to overwrite, take the old .so file into another place first).
Also: have you tried with other browsers (Konqueror, Epiphany, Opera, ...)? Not every browser works with every site (some browsers don't follow standards, some sites don't follow standards, ...), so you could get it work out with another browser. Worth a try, if you ask me.