Would you stay, knowing that your presence hurts the person that you love? Or would you leave to keep her away from that pain and hope that she would recover?

It's not really the physical act of leaving that is critical. The more important and more difficult part is parting emotionally. Is it advisable? Is it even doable? The sad part is whichever one chooses, pain is a necessary side-effect. More than the pain to one's self, it is the pain to that person that becomes unthinkable, unbearable.