It's often heard "you'll know" but that isn't comforting when you are dealing with a disabled dog. Often the underlying implication is that you "should" put the dog down. To those of us that love our pets dearly, the minor inconvenience of changing "diapers" or helping them walk is a minor compared to the alternative - losing our best friend.
While many dogs have difficulty adjusting to being disabled, others do not. Most are quite accepting of their limitations and adjust much better than people do to the same situation. This is one situation where it's not helpful or good to be anthropomorphic (giving animals human emotions and motivations). Animals have a much more realistic and sensible way of looking at disabilities. Actually, they are quite practical! Like us, their life force is strong and they want to continue - but unlike us they don't whine and complain about their lack of mobility, sight or hearing. They just make do!
Personality can play a large part in how accepting you and your dog should be. I'll give a couple of examples. We've had 3 males now with the same debilitating spinal disease in old age. Each handled it differently. First Homer - he was quite content to wander the yard once we helped him up. He would walk around, but when he fell, would just patiently wait until we came out and got him back up again. He gave up when he could no longer get up on his own. He could still sit, but not being able to walk made him give up. It was time.
Shadow lived his life with gusto. A very active and intelligent dog he was always into trouble! When he came down with the same disorder, he wanted to be busy then as well. He was very content as long as he could use his front legs to "walk" outside (with help from us in the rear). I really think he believed his back legs worked as long as we were there! He was still demanding and pushy, insisting on going outside in all weather and made the best of his situation. The time came for him when he must have felt he was losing control and started having severe separation anxiety. We couldn't leave the room at first, then his side. It became difficult to deal with because you do have to leave occasionally (to eat, go to the bathroom) and those times caused him great anxiety. It was time.
Hoover was our third dog with this same disease. Hoover had always been very easy going, very content. So when he got the same thing he followed Shadow's path of allowing us to "walk" him outside where he's sit under the trees and enjoy the summer weather. Fall came and we anticipated things getting worse, but he kept his spirits up even through losing bowel & bladder control, then eventually most use of his front legs as well. He was essentially a quadriplegic. But he was still happy - squeaking his toys, yelling at our other dogs, hanging out in the room with me while I worked from home. He was totally cooperative and tried to be helpful when we moved him (to avoid bedsores). He was content to watch and interact as much as he could. He was totally accepting of his disability. By the third dog, we also were more prepared and had a system in place that helped us care for this high-needs dog without too much trouble. I really don't think he considered himself disabled! In January, after a full 4 or 5 months of being totally indoors, his heart gave out. Overnight he had some severe problems that made it hard to breathe, and he gave up. It was in his eyes. He was ready.
So, the answer is the eyes. They will always tell you when it's time to make the ultimate decision. You must also consider yourself and your family as well - it's not fair to continue on to the point the dog is resented and a burden. He wouldn't want that either. In the wild, when a dog gets infirm and can't keep up, the pack will kill him. That's not to be mean, but to be kind. He knows he's a burden, and when he begins to feel he's a burden he will give up. The pack in caring for their disabled comrade will do what is best for the pack. Perhaps that means helping in some way - it's well documented that one dog will help another that is disabled. (We have Pod who is seizure alert dog and eyes for Chevy). Still, it's not about the individual it's about the group (your family). It's what is best for the pack overall, and your dog knows that and is accepting of that if he's really a part of your family. There are times it is more humane for the pack to attack and kill the weak one, than to let him die a slow and lingering death. Nature takes responsibility and care of it's own. Euthanasia is not cruel, but a natural extension of pack behavior and what dog's expect you to do when their time comes. You would are not doing them justice to let them linger in pain or misery.
One of the worst things I've seen is people who have sick, old or disabled dogs that dump them at the humane society because they can't deal with it themselves. It's an avoidance of pain for them. But in avoiding their OWN pain, they put a tremendous suffering on their pet. Would YOU want to die alone and abandoned? That is cruel and shirking your responsibility to your pet who has given you many devoted years. Take responsibility and even if it doesn't seem like it's time yet, the kindest thing you can do is be there while the vet puts them down humanely. Life is a circle, and the pack is everything to your dog. He would want his pack there to help him gently over the rainbow bridge.
Some clinics are more open than others to allowing the owner to stay during euthanasia. Some veterinarians are also willing to euthanize a pet at home. Others have come to an owner's car to administer the injection. Again, consider what will be least traumatic for you and your pet, and discuss your desires and concerns with your veterinarian. If your clinic is not able to accommodate your wishes, request a referral to someone that can.
You have many more resources than a pack has in the wild. If you have other dogs their natural instincts may be to kill the weak dog. If the dog is not that sick, you may have to protect him from your remaining pack. Don't consider that a reason to necessarily put the dog down. You are the pack leader and it is your job to find a way to keep a sick or disabled dog safe until you and that dog determine it's time. If this means keeping him away from the others, that may be what you have to do for his safety. Often one dog will take it upon him/herself to watch over the weak one and help him by being his eyes, ears, or just for moral support. Our boy Riggs was extremely comforting to Shadow and Homer in their old age - just being nearby at night, watching over them - and I think talking to them and letting them tell him their "war stories".
Not everyone can deal with a paraplegic dog - not everyone can deal with a blind, deaf or other problem dog - so it's not fair to make judgments as everyone who loves their pet will make the right decision for their family and the pet. If you can work with a disabled dog, the rewards are wonderful. But it's never easy to make that final decision.