These small movements lead to metal fatigue that weakens the structure in the long run. This is similar to folding an iron wire over and over, which ultimately winds up breaking. We could thus imagine that it would take about a thousand years for take the Tower down.
Why was Eiffel Tower almost demolished?
The Eiffel Tower was supposed to be torn down after 20 years. The tower was built with the intent of showing off France's industrial prowess during the World's Fair, but the plan was to tear it down after 20 years. However, Eiffel cleverly put a radio antenna and wireless telegraph transmitter in the tower.