I am not using Air Display so cannot be too sure how to help you here, but suggest you try Air Display with something other than EFB - choose something simple - and see if the touch screen works there. If not, you have an issue to raise with the Air Display support.
I am using DisplayLink, a free package for both the PC and the iPad, and it works beautifully with EFB. However it does not support touch screen input, so the iPad is "simply" a second display and you use the PC's mouse to control the EFB window displayed on the iPad. Just as you would with any multi display setup. Check it out at http://www.displaylink.com/support/downloads_ipad.php
On this subject, there is an item in the FAQ here relating to the iPad. I would like to see a reference to DisplayLink included in that FAQ item, especially as DisplayLink is free, and it does work!