Latest ASIAIR 2.1 (firmware 11.05):
Are you using the cables that came in the ASI585 box? Be sure to throw out all ZWO cables. Never ever use a ZWO cable for USB or for power. They ship the cheapest untested junk with their expensive devices, and combined with the poorly designed (apparently no design margins) USB hardware in the ASIAIR and their cameras, causes many of the cables to fail to work.
Also, don't forget to supply 12V power to the camera even if you don't need the cooling.
Plug the camera into a desktop computer running ASIstudio, see if that works -- the computer has proper USB hardware, unlike the ASIAIR.
Chen