There are medications that can help with the pain. it sounds like she is having trouble getting around daily, and then gets significantly worse when exercised. I would suggest looking into medication, it could greatly improve her quality of life. Rimadyl is one medication, Metacam is another. When my lab got to an older age, I thought she was just slowing down. However, I left her with my parents when I went out of town and they took her to the vet as they noticed just how much she had slowed down (which was not as apparent to me, since it happened over time and I lived with her). The vet prescribed Metacam, and when I came home, it was like a whole new dog! She acted like a young dog again with the medication. It was truly beneficial. If your dog can not do the stairs even when the max dose of pain medication is used, then I might consider euthanasia. But your dog sounds like an excellent candidate for an arthritis drug.
Also, about Gluscosamine. Most dog foods do NOT contain enough to be therapeutic. Orijen Senior contains 1400mg/kg Glucosamine and 1200mg/kg of Chondroitin. Your dog would need to eat about 8 CUPS of Orijen a day to get that amount. Cosequin, a popular brand of Glucosamine and Chondroitin tablets for pets, recommends dogs over 50 lbs and under 100lbs should get 1,500 mg of Glucosamine and 1,200 mg of Chondroitin daily for a therapeutic dose. Unless your dog is eating 8 cups of food every day, she's not getting a therapeutic dosage.
As far as Aspirin, its great for the dog that only needs it occasionally. It sounds like your dog needs to move to something stronger though. Just because she's near the end of his natural life span doesn't mean that some meds couldn't help make her more comfortable until she passes on. I would revisit the issue with your vet- tell him that she's slowed down significantly, that the dog still begs to go on walks but if you do bring her, she literally cant walk afterwards, and that you've thought about euthanasia because her quality of life is diminishing due to the immobility. I wouldn't be surprised if medication helps a great deal- it might be that she does nothing all day not becuase she is old, but because it hurts too much to move. Meds can help with that, and make you both happier.