Because it doesn't stop working. A tall chimney still works.
It works during the day just fine, as long as the atmosphere is sufficiently unstable, or you can concentrate sunlight to get excessive heating at the base of the chimney.
But the web site linked here claims that their super-chimney can work forever by exploiting the temperature difference between the bottom and top of the chimney. This is nonsense. It justifies this by saying that the air in the chimney somehow doesn't expand and cool as it rises the way that air outside the chimney does. This is bullshit.
Your logic seems to make sense but how would you explain the purported chimney effect that has been observed on https://en.wikipedia.org/wiki/P%C4%B1narg%C3%B6z%C3%BC_Cave#... which is a cave with openings at low and high elevations and the difference in temperature is claimed to create "constant wind of up to 166 km/h"?
It works during the day just fine, as long as the atmosphere is sufficiently unstable, or you can concentrate sunlight to get excessive heating at the base of the chimney.
But the web site linked here claims that their super-chimney can work forever by exploiting the temperature difference between the bottom and top of the chimney. This is nonsense. It justifies this by saying that the air in the chimney somehow doesn't expand and cool as it rises the way that air outside the chimney does. This is bullshit.