Tough question, one that occurred to me as well.
Under the same circumstances, I'd want my child to live too and when I had spent all my resources, I'd still want him to live, though the decision to keep trying, would no longer be mine to make.
An ecmo machine is not intended for long term use and creates medical problems of it’s own. It is used to relieve stress on the heart and lungs allowing them to heal. From reading this and the rather limited medical info given, it sounds like that is not happening.
It is a difficult and painful decision for parents to make. Dear friends of ours made it with the prayers of FReepers asking God for wisdom and comfort.
I pray for the child and his family.