Harpack and ice is tricky to hold an edge at the bottom of the turn when carving. All forces come together here to want to throw the board to the outside of the turn...gravity, momentum and centrifugal force. A few things you can do to help increase your edge hold here:
More angulation, less inclination:
The more you incline (lean) your body toward the inside of the turn, the more force is directed to the outside of the turn horizontally. This adds more stress to your edge hold. By using more angulation of the ankles, knees and hips. you can maintain the high edge angles needed for good carving, yet keep you body over the top of the board exerting all force vertically down onto your edge thus providing superior edge hold.
Aft shift of your weight through the turn:
It is always the tail that starts to skid first when a carve begins to fail and turn into a skid. At the critical point in the bottom of the turn, shifting your weight slightly aft of your centered stance, weights the tail and increases the edge hold.
Flexion and extension:
Start into each carved turn low by using good down unweighting movements to make your edge changes. As the turn progresses, slowly extend through each turn. This rising through the turn applies additional downward force locking your edge into the snow better.
Work the top of the turn:
Complete each turn to manage speed and make the edge change earlier so you get your new edge set before the board enters into the fall line. By working the top of the turn, you can get the edge engaged early and even use the top of the turn to do a little braking early so you don not enter the bottom of the turn with so much force.
The reason we have more difficulty maintaining a good quality carve heelside is a result of our ankles for the most part. When toeside, we have great range of movement and can use our toes to "soften" of "dampen" the ride a bit. On heelside, our ankles simply don`t work that way. The trick is to loosen up the knees more to get the same level of shock absorption. This is where more angulation also helps us out. When you carve heelside, allow a bit more looseness in the knees to absorb any vibrations or chatter so you keep the board in positive contact with the snow.
Play around with these concepts and you should see that when you get the timing down, things will click for you...