Archie Battersbee's parents have lost a bid to challenge a High Court ruling that denied his transfer to a hospice at the Court of Appeal.
It comes after a High Court judge ruled that the boy, 12, should remain in hospital until his life support is withdrawn.
The Court of Appeal confirmed on Friday shortly after 6.30pm that permission to appeal had been refused.
His parents have fought a long-running legal battle over the withdrawal of his treatment, which ultimately failed on Wednesday when the European Court of Human Rights refused to intervene.
Their focus then shifted to trying to get their son moved to a hospice, but in a ruling at the High Court on Friday morning, Mrs Justice Theis concluded it was not in Archie’s best interests to be moved.
The boy has been in a coma since he was found unconscious by his mother in April and is being kept alive by a combination of medical interventions, including ventilation and drug treatments, at the Royal London Hospital in Whitechapel, east London.
Earlier on Friday, the High Court was told that Archie was in such a grave condition that moving him to a hospice carried a “significant risk” he could die during the journey.