When the game shows Little Mac's KO scene, press the 1 and 2 buttons together as soon as it starts. This will cause Mac to stamp his foot on the ground and gain one final burst of energy, letting him continue the fight and deny the KO.
The trick can be used at least once per fight. This can not be used on normal knockdowns; it can only be used during Mac's KO animation.
It should be noted however, that whether or not it will work is completely random, even when executed properly by the player.