There are so so many situations that can result in a low energy society. And there are so so many ways humanity can and will react to the transition from what we know now to a low energy society. But assuming it's a soft powerdown, and slower change from high-to-low energy society, you will have time to adjust. Having time to adjust, and internet persists, DMD network will survive guaranteed.

Assuming a fast societal change with less time for humanity to adapt (limited nuclear strikes, exploding calderas, volcano eruptions, virus outbreaks, meteor strikes, AI-war which comes to a stalemate etc), colonies of humans will survive, and if a rudimentary internet exists between the colonies, DMD network will survive and carry on.