That throttle comes with toggle switches; Can those be turned off so they don't press a button, or is each state a separate button?
If more than two buttons are held down (in total, on any combination of mapped joysticks, E.G. one button on a joystick, another on a throttle controller), the testing dialog will not show any button presses, however commands should still trigger when their assigned button is pressed.
To assign a button while multiple buttons are held down already, you should be able to use the refresh button on the "Select Joystick Buttons" dialog to make that dialog functional again (the refresh button should also work on the testing dialog).
EDIT: VoiceAttack beta v1.8.6.9 contains a fix for this issue, and can be downloaded
from the website