Factors

This depends on a whole lot of factors, but it mainly hinges on how wet it is where the skyscraper is located and if it uses rebar. Once the windows started breaking due to lack of maintenance and moisture really gets in, those which use rebar would start collapsing within 30-50 years. All-steel constructions (no rebar) built very conservatively like the Empire State Building might last 200+ years before collapsing.

However, if in a dry area where there is much less moisture with a neutral climate such as Los Angeles, even rebar skyscrapers might last 200+ years before they fell over.

So post-apocalypse thereโ€™d never be any truly ancient skyscrapers remaining. Most would be gone within 50 years, and within 300 years all of them would no matter where they are located. Without constant maintenance โ€” like most things โ€” even skyscrapers are quite evanescent.