The parents of Alfie Evans have failed in an 11th-hour attempt to persuade judges to let them move the terminally-ill youngster to a foreign hospital.
Tom Evans and Kate James, who are both in their early twenties and from Liverpool, say life-support treatment should continue to be provided to their 23-month-old son.
Specialists disagree and judges have concluded that continuing to provide life-support treatment to Alfie is futile and not in his best interests.
Doctors at Alder Hey Children's Hospital in Liverpool stopped providing life-support treatment late on Monday after Alfie's parents had lost two rounds of fights in the High Court, Court of Appeal, Supreme Court and European Court of Human Rights.
But the couple, who want Alfie to be flown to a Rome hospital, mounted a "one last chance" challenge.
The couple said their son had confounded specialists' expectations by continuing to breathe despite being disconnected from a ventilator and provided with only palliative care.
They said he had defied doctors' expectations and his continued survival amounted to a significant change of circumstances which merited a review.
A High Court judge ruled against them on Tuesday and three Court of Appeal judges dismissed a challenge to that decision on Wednesday.
Lawyers representing Alder Hey bosses said Alfie's condition was irreversible and there was no evidence that it had changed.
They said the fact that he had continued to breathe unaided might have surprised members of the public but had not surprised specialists.
Barrister Michael Mylonas QC, who led Alder Hey's legal team, said it had never been suggested that Alfie would die as soon as life-support treatment stopped.
He said the couple's challenge should be dismissed.
Barrister Sophia Roper, who represents Alfie and takes instructions from a court-appointed guardian, agreed.
Lord Justice McFarlane, who headed the appeal court panel of judges, said Alfie's parents were trying to take "one last chance".
But he said there was no prospect of the couple's challenge succeeding.
He said Alfie was in "the middle" of a palliative care plan.
The two other appeal judges, Lady Justice King and Lord Justice Coulson, agreed.
Lady Justice King said there was "acceptance" that Alfie was dying.