The parents of a 21-month-old boy may appeal to the Supreme Court after losing the latest stage of a life-support treatment fight.
A High Court judge has ruled that doctors can stop treating Alfie Evans, against the wishes of his parents Kate James and Tom Evans.
Three Court of Appeal judges upheld that decision on Tuesday.
But lawyers representing the couple said they might ask the Supreme Court to consider the case.
Judges have heard that Alfie, who was born on May 9 2016, is in a "semi-vegetative state" and has a degenerative neurological condition doctors had not definitively diagnosed.
Mr Justice Hayden had analysed the case at hearings in the Family Division of the High Court in London and Liverpool.
Specialists at Alder Hey Children's Hospital in Liverpool said life-support treatment could stop and the judge said he accepted medical evidence which showed that further treatment was futile.
Alfie's parents, who are both in their 20s, had challenged Mr Justice Hayden's ruling in the Court of Appeal.
Lord Justice McFarlane, Lord Justice McCombe and Lady Justice King, who had examined issues at a Court of Appeal hearing in London on Thursday, dismissed the couple's challenge.
Barrister Stephen Knafler QC, who is leading the parents' legal team, said "the State" had wrongly interfered with "parental choice".
He said Alfie's parents wanted to move him to a hospital in Europe but Mr Justice Hayden's ruling had prevented them from doing that.
Lady Justice King read out the appeal court ruling.
She said Alfie's parents were "unable to accept what movements in Alfie they see are not positive responses".
She said medical evidence showed that Alfie was "deeply comatose" and "to all intents and purposes unaware of his surroundings".
Alfie's father wanted to move him to a hospital in Rome then, if necessary, to a hospital in Munich.
Lady Justice King said he was passionate and wanted to "fight on with Alfie's Army".
But she said he had "no clear plan".
She said Mr Justice Hayden had considered all evidence presented to him and added: "(The judge) could not have done more to ensure father and mother had every opportunity to express their views and have them taken into consideration."