When do you put an old dog down?

Me, too. And to the OP, my sympathies for your situation. The tough thing to do is usually the right thing to do. You'll know what that is.

I have had to do this twice this winter, about a month apart.

The first was my Gordon Setter who had been shot early in his life by a neighbor. The shot broke his jaw, and ten years later the arthritis was locking his jaw. He was in constant pain, and whined a lot day and night. The second was my wife's Chessie, who we knew had bad hips when we rescued her, but she lived to be 16 years old before I couldn't stand to see her suffer anymore. When they get to the point that they can't do their "job" anymore (whatever they self-appoint themselves to do), you can see in their eyes that they are frustrated and depressed.

We made her suffer more than she should have, because my wife couldn't let her go. That was selfish of us, and she deserved better.