They died because they were imprisoned, in Westeros. They were kept chained, because after the Targaryens had conquered the land, they could no longer fly free, burning and eating whatever they wanted. And so they grew smaller, and smaller, until they died out.

[ she's wondered the same thing, and so she has a thought answer ready. ] The dragons here are smaller, more like horses. Perhaps they would do for cavalry, but they couldn't burn a city by flying over it once. But it's a reasonable concern.