Plato's age at his death isn't all that surprising. As the wikipedia article says, a life expectancy figure for a given pre-modern society is not the same as the actual number of years a child born into that society is likely to live. The number is an average that is heavily skewed by the high rates of infant mortality that characterise such societies. Children are more vulnerable to disease and deprivation than adults, and in the absence of modern hygiene or medicine, many of them would not make it to adulthood. Those who did, however, could generally expect to live to the age of 60 or over. There were enough people over 60 in Classical Greek city-states for the Greeks to designate that age as the cut-off point for military service. At Athens, old men were known to haunt the courthouses, hoping to make an extra buck by doing jury service. Sparta had a council of elders (the Gerousia) which consisted entirely of men over 60; competition for election into this council was fierce.

No one would therefore have found it particularly odd that Plato lived to the age of about 80. To my knowledge, no ancient source comments on the fact. Indeed, he was hardly the oldest man of his time. King Agesilaos II of Sparta, lame from birth but forced through the brutal Spartan upbringing, was severely wounded in battle at Koroneia, and almost succumbed to blood loss after the botched treatment of an infection on his leg; he died in 359 BC on his way back from a military expedition in Egypt, aged about 84. The playwright Sophokles was one of Athens' greatest tragedians with a career spanning over 50 years; he died when he was about 90. Most impressively, the Athenian orator and writer Isokrates wrote the last of his treatises shortly before his death in 338 BC, aged 98.

There is no doubt that all of these men were able to attain such a ripe old age largely because they were members of the elite. The ideal of rich Greeks was to live a life of leisure - in other words, they openly avoided doing any work. Instead, they devoted themselves to whatever they pleased (hunting, poetry, horse riding, sports, philosophy, drinking), which would have helped them live longer than the average farmer or wage labourer. They cultivated an ideal of physical perfection that would have encouraged at least some of them (especially the young) to exercise frequently and keep an eye on their diet. In addition, they had access to the finest foods, as well as the best medical care available. Unlike many people in their time, they probably never had to go hungry.

A life like Plato's, free from want and wholly without hard labour of any kind, probably helped him live long without losing his faculties. The Greeks generally thought a life of moderation and exercise would result in mental and physical health, and they were of course correct - even if most of the rich fell short of this ideal.