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Babu Chiri Sherpa holds the record for the longest time spent on the summit of Mt Everest, about 21 hours. He did so on purpose, and people usually don't spend more than about half an hour at the summits of mountains taller than 26,000 ft (7,900 m). There is a story about a climber who spent 4 days above 26,000 ft on Everest however, who reportedly survived without lasting effects.

Mt McKinley (Denali) and Aconcagua don't reach what is referred to as the "Death Zone", but their summits are still at an elevation where you can't survive forever. I wonder what the record for the longest stay on each summit is.

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This does not answer your question directly, but does shine some light on how long people can do demanding work, physically and mentally, at similar altitudes.

According to Thin Ice: Unlocking the Secrets of Climate in the World's Highest Mountains, by Mark Bowen, three climatologists and engineers spent more than 50 (repeat 50) consecutive days at 19,500 feet (5950 m) drilling ice cores in Peru on Huascaran's Garganta Col. The work of drilling is physically demanding, and record keeping and preliminary scans of the cores requires a clear mind and exact observation.

Aconcagua is about 3,000 feet (900 m) higher, Denali is slightly higher and has a much harsher climate, and the three men had a history of prolonged drilling at high altitude, so this answer is only indicative, not definitive.

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    There is a story about two people who spent two years at almost 20,000 ft altitude (but I dunno where; if it was around the equator, the barometric elevation would have been actually lower, somwhere around FL180 (18,000 ft)). But Aconcagua isn't close to the equator, not to mention Denali. Denali is likely about the same barometric elevation as Aconcagua due to its extreme latitude and subpolar temperatures.
    – Johannes
    Commented Sep 10, 2023 at 5:45

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