My brother, however, had a daughter born a month early and it was clear early on that she had suffered some sort of brain damage late in the pregnancy. She had no sucking reflex and the EEG showed definite impairment.
The hospital recommended turning off life support, but my brother and his wife refused. The baby eventually stabilized after a couple of months to the point where they were able to take her home, but the baby had to be tube-fed and have her lungs aspirated several times a day.
She never showed any signs of development although her parents preferred to live in a state of denial. Finally, she died in her sleep at about 10 months of age.
From my perspective, I think the parents should have listened to the doctors and pulled the plug during the first week. Instead, they incurred hundreds of thousands of dollars in medical expenses and spent nearly a year providing 24 hour care for a baby who probably wasn't really aware she was alive. It dragged out the grieving process for months and I can't think of a single good thing that came out of it.