Another suggestion that's already been mentioned, is that maybe the archers wanted to fail in order to leave the ranks and go home. It's not as if they all expected to win at Agincourt, they were outnumbered and tired from their retreat from the French. I would imagine the temptation to desert would be high, but they'd need to find some sort of honorable excuse to do so. That's if this "test" thing ever actually happened. If I thought I was going to get ridden down by a French knight or die from dysentary, or in general not have such a fun time, I would think about desertion, just need to figure out a way to get away with it without being caught and hanged, or whatever the execution was for desertion for the English army back then.
The Duke of York having a cap on how many people can be in his elite unit of archers makes sense too, as far as can he afford them.
