Hi James,
Also, you may contact your developers and ask them what protocol is used by your JNLP application and check here (https://support.smartbear.com/viewarticle/78569/) if LoadComplete can record it.
Also note that JNLP applications can (or always do this?) run in its own container outside of web browser. So you may also try to check that LoadComplete is also not blocked from recording traffic from your application by going through this help section: https://support.smartbear.com/viewarticle/78647/.
One more idea is to use, say, Fiddler application (http://www.telerik.com/fiddler) to get the traffic from your browser and JNLP application to get an idea of what might prevent LoadComplete from recording JNLP-based traffic.
