"Personal failing" has idiomatic meaning, it specifically refers to things which are that person's fault. Medical issues generally don't count as "personal failings". If you did something wrong that caused a medical problem, that could be a personal failing. For instance if your organ failed because you drove your motorcycle too fast and crashed, that could be described as a personal failing.
Oh yea, my kidney definitely died because of a lack of willpower. Indubitably.