This is, at bottom, a type of custody case. If there were no limit on appeals and 'new evidence' every custody case would stay active until the ward was grown or dead. No one would ever give up and no decision would be final.
So9
I can see your analogy, but there is no perfect one.
No system should allow somone who credible (even "last minute") evidence shows is conscious to be starved to death on the premise she would never be conscious again.
It's like burying someone we know is alive, even though a court found them to be dead (after making findings of fact on the subject).