I have not had a chance to read every reply to the OP, but I think that most medical interventions are not extraordinary when it comes to saving a life, whether of an infant or of an adult. I do, however, believe in palliative care when, save an act from God, the child will clearly die very soon (eg, anencephaly, where the baby has no brain). Most premature babies do not have these kinds of birth defects, though, so every possible avenue should be taken to prolong their lives. Who are we to say who “suffers” and who does not? Don’t we all suffer in life? Medical care is, ultimately, a futile endeavor, since we will all die, either now, or tomorrow. My dear grandmother suffered tremendous pain at the end of her life, but I do not think it was cruel to take her to the doctor and ensure that she received her medication. When she knew it was time, she decided to have a ‘Do Not Resuscitate’ order, and moved into hospice, where she received palliative pain treatment until she passed peacefully away into the arms of God. The same can be said for an infant: physicians and nurses should give them the best possible treatment, and when death is imminent, should provide hospice care for the child.
Personally, I think the “let them die” approach is horrifically cruel, and a direct outgrowth of our abortive culture. The difference between this approach and the hospice approach is that hospice acknowledges that all best efforts have been tried to heal the person and save their life, but that there is a reasonable belief that death is imminent, and so only palliative care is given. Without trying as much as possible to save the person, “letting them die” is euthanasia.