First thing you should know is that Jinitiator is no longer supported by its creator, ORacle:
http://blogs.oracle.com/stevenChan/2008/02/jinitiator_13_to_be_desupporte.html
So you cannot expect Cisco to support technology abandoned by the originating vendor.
You are most likely running it through rewrite engine (accessing http link through ASA WebVPN portal). Like this it has very slim chances to work. This is because ASA rewrite engine cannot properly rewrite all the content needed for this to run.
Generally in scenario where rewriter fails we use smart-tunnels as alternative.But even with this it is not going to make much difference. It will only on IE browser where smart-tunnels run as ActiveX. If you use any other browser it will load Java flavor of smart-tunnels and again the JInitiartor based app will not be able to work. It is known fact that Jinitiator has issues and fails to run if you start some other Java applet before it. You can verify this if you open a Firefox window and in one tab first go to www.time.gov (and click on a timezone to load the clock Java applet) and in the other tab you try to start the Oracle Forms application directly (without ASA in the middle). You will see that it will fail to start and this has nothing to do with Cisco ASA. This is caused by conflict between two JREs and it can be avoided by migrating to Sun JRE to run Oracle application.
You only solution is to migrate to Oracle Java (ex Sun Java) based application, as Oracle suggests.
