I've worked at a number of startups and usually, once the technology is picked for the initial stage project, it takes a monumental effort to ever upgrade it. Obviously, there is no reason to upgrade to the "next hot thing"; however, there are lots of situations where it seems like the way to do it.
For instance, moving from Angular 1 to Angular 2 or React. Using libraries like Redux to deal with data flow. Or using TypeScript for type safety.
Even larger jumps are moving from one language or platform to another.
Angular 1 to 2, on the other hand, wasn't designed to be an easy transition. They're very different frameworks.
So to answer your question, I use a new technology that allows gradual transition (when possible), or I use "free" time to do a full rewrite. If I find enough time to make something stable enough to move into production, great; otherwise, I've demonstrated empirically that we don't have enough time to invest in a transition.