Among all human organs, which are less prone to illnesses, failure, cancers; found in better condition than others at old age death, or rarely give/harbor health problems ?

 

To what would you attribute such endurance ?

It depends, to some extent, on how you define "organs". The word means literally (going back its Greek origin) a " working thing". So such things as hearts, lungs, livers, kidneys are obviously "organs", because they perform obvious work in the human body. Pumping blood, circulating oxygen, filtering wastes and so on.

 

But what about things like bone and teeth? They also do vital jobs - supporting the body and enabling us to bite food. Can they be regarded as "organs" If so, they're probably the most long-lasting bits of the human body. They even survive death for ages. Consider the role bones and teeth have played in the development of sciences like Paleoanthropology.

 

However, bones and teeth do give living humans health problems. Our teeth decay, and our bones are more likely to break, as we get older. Therefore they don't really satisfy your OP.

 

Could the definition of "organ" be extended to "fingernails"? If so, I'd say they probably best meet your requirement of being "less prone to illnesses, failure, cancers, found in better condition than others at old age death, and rarely give/harbour health problems".