Why do great chess players fade with age?

All athletes fade as the body ages.
Chess players fade as the body ages.
Therefore chess players are athletes.

All dogs are animals.
Cats are animals.
Therefore cats are dogs.

But to answer your question, you can't calculate as well and you can't handle stress as well.

Don't ever underestimate someone just because their older doesn't mean their Tiger Kung Fu isn't dangerous!

What IF life extension became reality for the masses in this lifetime? e.g. living to 200-300 years? 50 years would still be a teen...

That would be great.  Transhumanism has so much potential for our species though some naysayers want to impose their will on the rest of us so there might be a small window at least here in the West.  I wouldn't want to have to go to China for transhumanist operations. 

haha

Stress? I thought chess was supposed to be fun.

Not if your games last 6 hours and you're playing for one million dollars

I reckon so.

A reduction in short term memory is well established and scientifically proven (not just anecdotal) in older people. So if they can't remember their train of thought in a particular line (or if it takes them longer and they make more mistakes), they won't be able to calculate as well. 

Their understanding of the positions and analytic skills remain however, possibly even improve if they keep reading and thinking about the game. They have less resources to work with so they have to be more economical in their thinking. And unless they get a really bad brain disease will still pack a formidable punch until death.  

I think also that chess works better as a (perhaps dubious) way of discovering things about yourself and about life, it's not really experiencing life in itself. People may not want to spent their last days playing a board game, it's not like they have a dream of becoming a great player in the future. 

Very well said sir.