Our current understanding seems to be that the electrical activity of the brain is what maintains the mind-consciousness system. (From a physical/materialist pov)
Nah, there have been cases with short temporary flat EEG that came back to life, which is why the guidelines specify the duration for declaring someone dead in this way.
Those people suffered no memory or identity loss, so electric activity is not related. Connectome structure and tuned bioelectrical responses based on cell cytoplasm gradients, receptor structure and number tuned by a bunch of either RNA or proteins the most likely candidate. So the better analogy is it's like flash memory, left unpowered but running for too long the neurons will change.
Restarting the brain from that flatlined state is therefore possible, we just don't know how to do that properly. Most importantly, it won't do any good if the brain is damaged and is rarely useful.
Life must be sustained, once it is lost, it seems that there is a bell that cannot be un-rung.
However, our understanding of how much energy it takes to sustain life at a minimum seems to keep decreasing, like higher efficiency RAM in low-power mode.