As Another poster explained in a discussion about the case of Jahi MacMath, the teen who died but whose body is being kept on a ventilator, the heart is not directed by the brain to beat, bit it does need oxygen. So someone who is brain dead and still ventilated will continue to have a beating heart for some time–I am not sure they have ever kept someone in this state on a ventilator for an extended period of time.
However, because the brain is not sending out signals, there are bodily processes which are not continuing, and so the body is deteriorating.
Extraordinary means can be refused if ithere is insufficient chance of good results or if there is a burden on the patient or others, which can include financial.
It would seem that in this case, the father’s request is moral, given the experimental nature of the undertaking, and the potential burden, emotionally and financially, to the family.
The mother has died; the baby would die as a result of the mother’s death, not as the result of a positive action on the part of anyone.