We cannot say that. We can’t just ask an animal, “Have you lost the will to live?” That is euthanasia. The same as assuming your grandmother “Wouldn’t want to go on like that”. We cannot know since they cannot speak.
My last dog died at home. I’m glad she did, where she felt safe and comfortable and didn’t have the life forced out of her, she just let go. That is a peaceful death.
Right now I have a dog at home that is only 11 years old, but 100 lbs and not in good health. Sometimes she slips and falls and we have to pick her back up again. She spends most of her days on her doggie bed and only getting up to get water. And yet, when my brother’s friend came to visit today, she wagged her tail and him and barked hello. The last time she fell and I helped her up, she leaned her head against me, like she’s always done, like she’s giving me a hug. She loves having her ears rubbed. Who am I to tell her her time is up? That is up to God. He will call her on His own terms. I have no business forcing her through heaven’s door.