What if a society's collapse is a feature of progress, not a failure of it? Popper argues that open societies thrive on questioning and closed ones stagnate by suppressing it. But this introduces the contradiction that openness can't be preserved by any fixed set of rules as rules rigid enough to structure a society inevitably devolves the openness they're meant to protect.

The optimistic read of that problem is that the devolution is itself the corrective. Athens outpaces Sparta through openness, devolves, falls. Rome's republic succeeds it, devolves, falls. Promoting growth is then: promote openness as a principle and accept that when a society devolves, its failure clears the way for selection for increased openness.

It seems to me that the open society is in a perpetual state of trying to outrun an endless sequence of problems: would-be invaders from closed societies, internal activists who would rather close down the society in the name of stability, exhaustion of resources on the planet, solar system, and so on, the inevitable asteroid impact or supernova, etc.

And the idea is that this endless sequence of problems exists regardless of how open your society is. So even if you were able to implement a perfect set of authoritarian rules to establish a stable closed society with the technology to capture all the resources from the solar system and redirect all dangerous asteroids, well crap, you still weren't innovative enough to stop the supernova from killing everyone 200 million years later.

Worth noting that Popper himself would probably reject this as he explicitly argues history has no meaning or direction. I'm inclined to see this view as in tension with the idea that openness promotes growth combined with the idea that growth is self-selecting

Why can't the society have evolving rules? Looks like your "rules rigid enough to structure a society" phrase denies this is possible, for no reason.