Check out page 309 of the AIR Dev Guide "Only one instance of
an AIR application is started. When an already running application
is invoked again, AIR dispatches a new invoke event to the running
instance. It is the responsibility of an AIR application to respond
to an invoke event and take the appropriate action (such as opening
a new document window)."
It looks like we have to handle this InvokeEvent.INVOKE event
and programatically create a new instance of the application.
If anyone's done this already an example would be a big help
as this will be a VERY common use case.