Death by natural causes
seems to occur for three main reasons:
1) The body is not adequately maintained and things eventually break. Examples of this are the hardening of the lenses of the eyes (presbyopia) and arteriosclerosis.
This could be solved either genetically or by cloned organ transplants. The latter would involve growing whole organs, and replacing the originals as required. Fixing the brain is obviously more complicated.
2) A failure event is genetically scheduled to occur. These are failures which occur almost like clockwork at a specific age. Examples are puberty and menopause. (I know that menopause isn't really genetically scheduled, but women are born with a fixed number of eggs, and menopause occurs after those are exhausted.) The methods used to fix these depend on what exactly each failure is.
3) Genetic material becomes corrupted over time, eventually breaking genes and making the DNA unviable. Some genes have more of a tendency to break than others, and not all mutations have a negative (or any) effect. This would require the implementation of some kind of enhanced genetic proofreading system, or routine cell-by-cell genetic resequencing from a genome stored in a computer, or something like that.
Picking small aspects of this research would make a hell of a project for someone, if they could secure the funding. I just hope that this stuff is figured out and works before I die of natural causes. Hopefully they can come up with some kind of age-regression therapy as well.
Another interesting possibility would be somehow converting a person's brain into digital data, then having a computer simulate it. The simulated brain would be, for all intents and purposes, an exact copy of its biological precursor. The electronic brain would possess the personality, knowledge, skills, and abilities of its biological precursor. The brain is then placed in a new body, and the body is changed as required. For all intents and purposes, and as far as "you" are concerned, you never died and are immortal.