Not recognizing the USB Memory is a bad sign (unless the USB memory itself is bad, which I doubt, given that nothing else works).
On the row of icons at the top of the ASIAIR app, the memory setup is the rightmost (with only the three white dots to the right of it). If you click on the memory icon, and if you have a USB flash card or SSD inserted, ASIAIR should allow you to choose between the microSD card (Disk), or the USB memory (Udisk). If the selection is not available, something is definitely wrong. Try this with nothing else (cameras, mount, etc) connected to the ASIAIR's USB ports, just in case one of the devices is causing the USB driver (software) in the ASIAIR to crash. Boot up the ASIAIR with nothing but a USB memory stick.
Perhaps you can download a fresh ASIAIR binary image (Google Drive) to a new microSD card (warning, it is rather large, and might take a while to download, depending on your Internet speed), and then transfer your license file from the old card to the new card, and try booting with the new card. There is a chance the USB Driver in the Raspbian is somehow bad on your microSD card. If that still fails, perhaps it is time to contact your dealer to get the ASIAIR replaced.
The binary image on the Google Drive is quite old and upon connection (between ASIAIR and your tablet), you will be asked to download the current firmware. Just to be sure that the copy of the firmware in your tablet's app is not the one at fault, you might also want to first delete the app from the tablet and download the app again from the app store.
Chen