Duet is quitting the Mac app to prevent OS X from forcing the computer into clamshell mode and locking the Mac's screen. After you wake up the Mac, Duet should automatically relaunch (if "Launch at Login" is enabled in Duet's Mac app preferences). If Duet doesn't relaunch successfully, you will need to launch the Mac app manually. If Duet still fails to reconnect, then try unplugging the USB cord and then plugging it back in or quitting the Mac app and launching it again.
We are working on improving this to make it more reliable and seamless.