When I come home, my dogs are excited to see me and they enjoy doing what they do. When that is no longer the case, it is time to let them go. If an owner's decision is based on not wanting to let their friend go, then it has probably gone too far. Prolonging a dogs suffering might help the family cope with it, but all it does is prolong an animal's suffering. If you look into their eyes and put your emotions aside, you know.
It really stinks when you lose a dog too soon. This happened to me twice. Once was an accident and once was a genetic defect; both were awful experiences.