I don't think it's more stable from a normal users perspective. It's only more stable simply because it doesn't get new features like standard Firefox, and is therefore easier to manage for large companies that can't afford to upgrade all the time.
Firefox Extended Support Release (ESR) is an official version of Firefox developed for large organizations like universities and businesses that need to set up and maintain Firefox on a large scale. Firefox ESR does not come with the latest features but it has the latest security and stability fixes.
ESR is mainly for businesses that don't have the time and/or manpower to test new features of the browser to make sure everything works with their setup every time there's a new release (every 6 weeks). This is for places that have hundreds or thousands (or more) of computers to maintain.
But of course, I don't know if this issue is related to ESR version. I don't see why it would be ...