
Andrew F. answered 01/15/21
Recent Tufts grad, math, computer science and SAT instructor
I guess it depends upon how you define "last."
Assuming the buildings are not impacted by anything they don't currently experience, like landslides, glacial erosion, etc, they'll just be weathered by rainfall and some wind driven erosion, plus eventually plant aided weathering, which would all act incredibly slowly.
For reference, pyramids over 3000 years old, partially constructed of granite, are still standing in pretty much their original form.
Polishing is just a surface treatment, and while you might notice that gone in just hundreds of years, it wouldn't affect the overall shape/resilience of the building as it weathers. Exact stone composition would however, and over time you'd see differential weathering - that is, some materials like granite would be much more resilient than others like marble, and would remain even as others more rapidly disappeared.
So, altogether, the rate at which the buildings erode is highly dependent on future landscape, climate, ecology, and myriad other factors, but big stone buildings could remain pretty much wholly intact for many thousands of years under good conditions, and their granite parts might erode just a few meters of exposed material over millions of years - long enough that other less predictable factors, like seismicity, ice ages, being buried by deposition, etc, would be dominant in their preservation.