This suggests that a country's policy can actually have some effect - a lot is beyond each country's control, but it's not hopeless.
This is based on reading Thomas Piketty's "Capital in the Twenty First Century" (I'm halfway through) - really good read if you are interested in this.
But stability doesn't really exist in the Universe - there's always a low degree of redistribution going on between the clumps (trade). And clumps can explode into smaller clumps (people die, and the property is inherited/distributed -- Immortal entities like corporations sort of escape this thing).
Wars (and revolutions) are indeed the major disruptor, as it evens out the playing field (mostly by removing a lot of the property so everybody's equally poor). It's in the interest of the big clumps to keep the little clumps from getting too desperate, or from getting any funny ideas about redistribution of property, or from possessing the ability/organization to act on those ideas.
In the absence of sudden and violent (thus unpredictable) disruptions, the big clumps can accumulate and plan sufficiently to slowly work their way into an optimum state: balancing their continuous growth (faster than the smaller clumps) with the suppression of those to stop them, without tipping the balance into revolution.
The longer a system of clumps stays stable, the less likely it's going to become unstable. Until you get an outside disruption (invasion, natural disaster, plague, etc.) which is usually how long-lived and stable societies ultimately perish.