there seems to be no limit on how many times i press the key so long as I do not click elsewhere (which in my case was this forum) while the scene is playing, If i do then the right arrow no longer has any effect - presumably because it is no longer being directed to the fullscreen part of the program.
Exactly, If you are using dual screens
and you interact with the mouse on the other screen, then you have taken the Focus away from the Full Screen Scene
You can give back the Focus to the scene by moving your mouse back to that screen, and using the right mouse button.