Have you tested this Aeon Labs Z-stick without the AWUSB, to make sure that works, providing that the issue is not with the Aeon Labs Z-stick?
Have you tried enabling the "Use Microsoft Device IDs" feature, to see if that resolves the issue? To do this, run the AWUSB Config Util (with Admin privileges), Disconnect the computer from the AWUSB, click File / Preferences, check "Use Microsoft Device IDs", click Save, then Connect the computer back to the AWUSB.
Do you have a standard USB 2.0 hub to troubleshoot with? If so, attach it to the AWUSB (to either of the two USB ports) and then attach the Aeon Labs Z-stick to the standard USB 2.0 hub. Does the Aeon Labs Z-stick work when it's connected this way?