Nothing is permanent.. at some point our planet will be burned when our sun becomes bigger , or the universe will end anyways either in big crunch or the opposite, everything being separated. Or universes will collide.. etc..
So if we are not talking about an eternal permanency, but a relative one... If the internet goes down, so will all the other established structures and all the global civilization as we know it. I think at that point we'd have a lot more to worry about than just this. In any case I dont think its in anyone's interest to make that happen.. Even those in power who might feel threatened by the blockchain idea, their lives and the lives of their family depend on the internet, there's no going back.
But even if we suppose that this could happen and that someone would pull the plug, there's nothing preventing the internet, or any potential successor, from working through a different network. Take the Firechat used in hong kong protests which could work without internet or phone signal as a small example of how things could change.
Now take projects such as the Outernet, and Maidsafe, and add this into the discussion. And now think of all the possibilities that we havent even thought of yet. All that is necessary is transfer of information for the block chain to exist, and this can be totally indistinguishable from any other information in a way that you cant tell appart what is block chain information from any other cryptographed information.
As for the energy necessary to run this, I dont find this in any way a criticism to the block chain idea which is being discussed here, any more than it is an argument against ANYTHING we use these days, including the food most of us eat.
Sure there are limits to our energy extraction/transformation process, but there's nothing preventing new solutions from being found. In fact, I'd argue that with the block chain technology, its MORE likely that people will invent and research viable alternatives in a way that cannot be stopped due to decentralization, as opposed to how hard it was to invent something and feel the pressure of big business to shut the idea down when they had an easy single target.
And yes, please do read the article