Court of Appeal judges have told lawyers representing the parents of a 23-month-old boy who has been at the centre of a life-support treatment battle that doctors are unanimous in concluding that the youngster cannot be saved.
Lawyers representing Tom Evans, 21, and Kate James, 20, have asked Court of Appeal judges in London to reconsider Alfie Evans' case.
The couple, who are from Liverpool, have already lost fights in the High Court, Court of Appeal, Supreme Court and European Court of Human Rights.
Lord Justice Davis, who is heading the three-strong panel of appeal judges, told lawyers that at the start of the hearing that doctors had agreed that there was "no hope".
He said: "We cannot have a kind of legal 'Groundhog Day' where you come back again and again and again on the same point."
A second appeal judge, Lady Justice King, said doctors' unanimous opinion was that Alfie "could not be saved".
Alfie's parents were not at the appeal court hearing, which is expected to end in the next few hours.
In February, Mr Justice Hayden ruled that doctors at Alder Hey Children's Hospital in Liverpool could stop treating Alfie against the wishes of his parents following hearings in the Family Division of the High Court in London and Liverpool.
Specialists at Alder Hey said life-support treatment should stop and Mr Justice Hayden said he accepted medical evidence which showed that further treatment was futile.
Court of Appeal judges upheld his ruling.
Supreme Court justices and European Court of Human Rights judges have refused to intervene.
Last week, Mr Justice Hayden endorsed a detailed plan put forward by Alder Hey doctors for withdrawing life-support treatment, after considering a number of issues at a follow-up High Court hearing.
The judge said detail of that plan could not be revealed because Alfie was entitled to privacy at the end of his life.
Bosses at a group which fights for Christians' rights, the Christian Legal Centre, are helping Alfie's parents.
Lawyers are asking appeal court judges to overturn decisions made by Mr Justice Hayden last week.
Alfie's parents last week said their son had improved in recent weeks and had asked Mr Justice Hayden to allow a new assessment.
Mr Hayden refused that request.
He said medical experts' unanimous view was that Alfie's brain had been eroded by disease and further assessment was pointless.
They also suggested that Alfie was being unlawfully detained or "deprived of his liberty" at Alder Hey.
The judge also dismissed that suggestion.
As the hearing began there were more protests outside the hospital by people dubbing themselves "Alfie's Army".
The hospital has increased security and urged the protesters to keep noise levels down because "loud and constant noise such as from car horns affects sleep and raises anxiety levels for our patients especially when recovering from procedures".
But a spokesman insisted that the hospital remained fully operational.
Appeal court officials said a judge had decided that Alfie should continue to receive treatment pending the outcome of Monday's Court of Appeal hearing.
Judges have heard that Alfie, born on May 9 2016, is in a "semi-vegetative state" and has a degenerative neurological condition doctors had not definitively diagnosed.
Alfie's parents have complained that "the state" is wrongly interfering with their parental choice.
They want to move Alfie to a hospital in Rome or Germany.