It seems to me, and I am totaly postulating here,
that the way to avoid, or lessen the shock would be:
1: don't snap, use a very sharp exacto knice and make a perfect cut, leaving as little internal tissue exposed as possible.
2: put a fungicide, and perhaps rooting hormone on the exposed portion of the rhiozome, then cover with live sphagnum if available.
3) Increase light, humidity, and all the other conditions these guys love. And hope for the best.