The family of Archie Battersbee have lost a last minute bid at the Supreme Court to stop his life support from being removed.
The case was returned to the Court of Appeal on Monday at the request of the government after the United Nations Committee on the Rights of Persons with Disabilities (UN CRPD) said it would consider Archie's case.
The Court of Appeal stood by its original verdict that removing the 12-year-old's life support would be in his best interests.
The family then applied to the Supreme Court for permission to appeal.
The judgment from the Supreme Court today said that the Court of Appeal had "made the correct decision" and that it did not believe there was "an arguable case that the Court of Appeal has so erred".
It added that today's judgment had been reached "with a heavy heart".
Earlier today, Health Secretary Steve Barclay said that the appeal to the Supreme Court should be refused and that the UN CRPD's request of a temporary stay on removing Archie's life support was "not binding" under international law.
"The notion that interim measures are binding has not been accepted as a facet of customary international law," government lawyers said in a submission to the Supreme Court on Barclay's behalf.
"There is no such consensus. On the contrary, the status of the committees' decisions is a subject of some controversy."
Speaking before the Supreme Court's judgment, Archie's mum, Hollie Dance, said she felt "betrayed" by the government's intervention.
"No authorities, other than the UN CRPD have shown any compassion or understanding to us as a family," she said.
"We want to say clearly, despite reports that Archie is 'brain-stem dead', that no medical professional has ever been able to prove that this is so.
"We as a family will keep fighting and want to say thank you for all the prayers and support we have received."
Andrea Williams, chief executive of the Christian Legal Centre, which is supporting the family, said: "When there are international protocols in place on issues as important as a person's right to life, we would expect the government to consider very carefully its obligations.
"Its response appears to simply fall in line with its domestic courts rather than to address its international obligations and the serious legal and moral issues raised in this case."