I look at it like this:
From what we know, the brain (and brain stem and to some degree the spine) is the center of, and contains the data for, your personality.
Your brain can theoretically be removed from your body, and if kept alive and given a means to communicate, your personality will still be intact. Certainly, it's a
popular science fiction trope.
I would not consider myself or any other person dead if they were surviving as a "brain-in-a-vat." I suspect this view would be widely shared.
This baby is the opposite case, or nearly so (it doesn't lack the entire brain apparatus, just most of it). So therefore, I would not consider it conscious or sentient, and therefore no more "alive" than a viable kidney removed from a cadaver for transplant.
This also nullifies the "what if we can grow a brain in the future" argument. If we could, that would be nice, and maybe in this mother's case we would. But it would be no different ethically than letting the body containing the damaged brain die, then cloning it, while fixing or preventing whatever caused the problem in the first place.
I think we can
all agree that this is a sad case, and that it's another great example of how life is full of -- to quote one of my favorite philosophers -- "some fucked up repugnant shit."