I have running the testcase and reproduce the issue which customer encounter.
But this mostly like a configuration issue in customer webserver side, the webserver is setup using client authentication, but even without client certificate installed on client machine, the webserver won't stop loading the page and applet, therefore the Java applet will still runs fine.
To simply testing that, open IE browser, trying to load this URL:
You will notice a "Choose a digital certificate" dialog box popup from IE browser (not Java at this point), and this dialog box is empty! click on OK button, the page will still load (by theory it should stop loading the page with error).
Please reconfig the https webserver to disable client authentication, which it didn't need by my understanding.