With hundreds of animals, this is a decision that we have to make several times a year and it is one of the hardest things we have to do. Our policy is that when an animal's quality of life has deteriorated to the point that medications are no longer helping alleviate pain, its time to euthanize.
It is very peaceful and we are there for several moments after life has ceased to make sure that their passing is with someone they know and trust, not a stranger. It is the right and merciful thing to do.
We will all face death someday and for our pets, we can make sure that their passing is peaceful and painless. Letting them suffer is not the compassionate thing to do.
Some people think that euthanizing is "playing God", I don't believe that, I think that it is looking out for the best interests of the animal in question.
God bless you as you make that decision.