As the founder of http://www.tripawds.com, Tripawds, the world's largest community of canine amputees and their humans, we always left folks know that while most dogs can live great lives on three legs, amputation is not right for every dog. A lot of it depends on their pre-existing health condition, their prognosis and their age.
We chose amputation for our Jerry, who was diagnosed with bone cancer at age 8. His prognosis was 4 months without chemo, 1 year with. We knew he had lots more living to do, he was otherwise very healthy and fit. So we put aside our pre-existing human notions of 'time" and "prognosis" and helped him alleviate his pain, which was the most important thing to us. After that, every day was icing on the cake.
Jerry survived two years with bone cancer, and no chemo.
Sadly, not every dog diagnosed with bone cancer is as fortunate. But what we tell folks is, if your dog is: you know your dog best. If your dog is otherwise healthy, even his age shouldn't be too much of a detraction to proceeding. We have seen dogs as old as 12 do just fine. Usually amputation is the only way to alleviate the horrible pain of bone cancer or an injury, and recovery is far worse on the humans than it is on the dog. Most bounce back within a couple of weeks, and while their physical activity will be slightly modified, for the most part they live the same healthy, "hoppy" lives as their quadpawd counterparts.
We encourage every pawrent to go with their instinct and talk to others who have been there. And get a second opinion if your current vet is advising you against it. Old-school vets are often very closed-minded comes to canine amputation, and many pawrents have found that a second opinion from a more progressive-thinking vet made the difference between saying goodbye prematurely and living a long happy life afterward.
Listen to your heart. You may find that your dog is stronger than you think.