Melnyk is about as committed to winning as cancer is to the body it develops in:
It sticks around, it wont leave willingly, it ruins the entire structure of everything around it and slowly kills off its host, and its only 'cured' by removing it directly or bombarding it with radiation/chemicals that annihilate its existence.
Now, I loathe Melnyk, but I don't wish harm on the guy, so the 'bombarding it with radiation/chemicals that annihilate its existence' options isn't the one. Dude needs to be surgically removed from the organisation. Unfortunately, the "doctors", (Bettman and the rest of the NHL brass and the other owners) are either unwilling or unable to remove him right now.