Tell her it's okay. This is so hard for kids (and adults!) but we are the stewards of our animals. That means that we must protect their comfort and quality of life whenever possible - even if it hurts us to do so. If there's nothing to be done to save him and let him live in comfort, your last gift to him will be ending his suffering. I personally believe that all animals and people are most at peace in death. That is what my parents taught me, and it has really helped in this life with loss. In death we are never hungry or cold or tired or achy. It's not such a terrible thing. I know you guys will miss him, but if they decide that putting him down is the best thing, prepare yourself for it and be happy for him that he gets to go to a better place.