The non-special keys are only available in the Adobe Integrated Runtime. I agree that it is puzzling why these constants are not available outside of Adobe AIR.
I think it has do with flash not letting you reference Keyboard.P when you're not using AIR, so it might work if you plug in the direct value of P rather than a reference to it... P : uint = 80 ... so try 80 instead of Keyboard.P and see if it works
I tried using 80 before, but it did not work. Recently, I tried that again. I used some trace functions to detect whether or not the event was being registered.
The outcome was that only the release event was being detected. Yet, the simply fix was disabling the keyboard shortcuts.