LONDON — Alfie Evans does not know it, but he is the subject of a national debate in Britain, international diplomacy and a bitter legal dispute. He is held up as a tragedy, a beacon of hope and an object lesson. And he might not live to turn 2 years old.

The hospital and doctors treating him in Liverpool say that Alfie suffers from a degenerative neurological condition that is certainly fatal, that he is in a semi-vegetative state and that the only humane course of action is to let him die. His parents, supported by the Italian and Polish governments and the pope, are not convinced that he is beyond hope, or even that the doctors understand his condition, and they want to continue his care.

On Wednesday, the British Court of Appeal upheld a ruling that not only approved the withdrawal of care and sustenance, but also prohibited his parents from seeking treatment elsewhere, despite an invitation to take him to a hospital in Rome. The decision is wrenching to the parents, the courts have said, but prolonging Alfie’s life would prolong his suffering, and so it would be contrary to his interests.

The staff of Alder Hey Children’s Hospital took Alfie off a ventilator on Monday, but defying expectations, he kept breathing on his own. The parents’ lawyers from the Christian Legal Centre have said they will continue their appeals.