I think we need to clarify something here. From a biomechanical standpoint, when putting out force or impact power to the front the rear heel is may be either up or down. But the key factor is whether you are pushing with the heel of that foot or the ball of that foot. In classical Karate (and I will assume Michael's Crane style as well from what he has written) the heel is actively pressed into the ground as the punch is delivered for a solid connection between the ground and the target. The heel stays on the ground the whole time because the puncher is pressing into the ground WITH the heel. In contrast, in western boxing one is not pressing from the heel, but from the ball of foot to get the momentum of one's body weight behind the punch. The heel may start down, but its going to come up off the ground because the force is being produced by pressing the ball of the foot into the ground NOT by pressing the heel into the ground. This is exactly what we see Mike Tyson doing in the video above.