Christine,
my sister in law had to make a similar decision with her dad, who has dementia and assorted physical issued, including falling. She felt like a failure at first, but is now coming to see that there is a limit to how much one person can do - and she went over that limit a while ago. I don't think you would call her a failure; I don't think you should call yourself a failure, either. Like my SIL, you are a wonderfully brave and caring person; but you are human, and we humans sometimes need some help. Best wishes for you both whatever your decision.
Maria