Leanna asked me to address this on the blog and, wow, that's about the hardest question I can even try to answer. All I can do is suggest the kind of things I think about, but by so doing I'm not saying that it's easy or clear or in any way black and white for me. This is a question that's immensely hard for everyone.
Here's what I generally think about, when I'm trying to make this decision:
Dogs don't fear death. They don't anticipate death, they don't know how long their lives have been, they don't feel robbed of years or impact. All of those emotions are ours alone. Dogs only know where they are right then; how they feel right then. As far as we know they have no idea of "I will get better" or "I am getting worse"; they only truly know how they are right now.
So, for me, when the dog has hit the point where the majority of his or her time is either painful or confusing, even if they are still eating or still able to walk and so on, I don't believe that keeping them going is very kind to them, recognizing who they are and how they depend on the moment they live in. I need to be sure that a dog can be made comfortable and that its world makes sense to it; as long as that's still the case I keep going.
One very useful rule, one that you put into place BEFORE the end – when you're thinking this may be getting close – is to list three things that show you that your dog is joyful. Maybe for your dog it's eagerly eating, chasing the cat, picking up the ball. The response time may be slow, but if the dog is still feeling enough engagement to do those things, she's probably still happy and comfortable. When two of those things have disappeared – she may still be eating but she shows no interest in the cat or her ball, or she'll still chase a ball but has stopped eating – it's time to let her go to heaven. The reason I say that you decide this early on is that it becomes incredibly hard to decide it later. You'll see any sign of the way she used to be and think that she is still "fighting" or words to that effect. You need to decide before it gets to that point.
Last – of all the times I have dealt with this, of all the people I've talked to, all the dogs I've wept over, nobody has ever said "We did it too soon." NEVER. But many, many say "We waited too long." Once the dog inside the dog is gone, it's time.
I don't have any quotes about the Rainbow Bridge or the Happy Hunting Grounds or anything like that. This is one of the few times I'll bring my theology training into play, and it's to say that the Bible tells us two things about animals: One, that their story is not our story; they have a different relationship with God than we do. So it should not surprise us that whether they end up in paradise isn't addressed; God figures we have enough to work on letting him get US there.
Second, he loves them very, very much. God is a fan, and I really do mean that. He pays very close attention to how we treat them, and he keeps track of every single one.
So while I cannot tell you whether THIS dog will end up in OUR paradise, though I rather suspect that he will, I can tell you without a shred of doubt that he is not going without a Very Important Person keeping a loving eye on him.