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Archie Battersbee's parents have lost an appeal with the Supreme Court - on the day his life-support was due to be withdrawn.
On Monday, Court of Appeal judges ruled that the 12-year-old's life-sustaining treatment should not continue beyond 12:00 BST on Tuesday.
His parents lodged an application to appeal the decision with the Supreme Court which has been refused.
Archie was found unconscious at home in Southend, Essex, on 7 April.
He has never regained consciousness and his mother, Hollie Dance, believes he may have been taking part in an online challenge when he suffered brain damage.
Doctors treating him have said they believe it is "highly likely" he is brain-stem dead and argued it is in his best interest for life-support to end.
A previous High Court ruling heard Archie's "every bodily function is now maintained by artificial means".
The family had asked judges to assess whether more time should be given for the United Nations Committee on the Rights of Persons with Disabilities (UN CRPD) to look at the case.
But the Supreme Court said in it's was "not persuaded that there is an arguable case that the Court of Appeal has so erred and accordingly refuses permission to appeal to this Court".
It also said the Court of Appeal "made the correct decision".
The ruling said it was "not clear that Archie has any more extensive rights in international law" nor was the decision to end treatment a "breach of international law".
"The panel reaches this conclusion with a heavy heart," the ruling said.
Before the decision by the Supreme Court, Ms Dance said the UN CRPD had been the only authority to "have shown any compassion or understanding to us as a family."
"We as a family will keep fighting and want to say thank you for all the prayers and support we have received," she said.
Archie's care was due to end at the Royal London Hospital in Whitechapel, at 14:00 on Monday, but the government asked judges to consider a request from a UN committee to continue treatment.
President of the Family Division Sir Andrew McFarlane, Lady Justice King and Lord Justice Moylan had ordered a short delay in withdrawing life-sustaining treatments until Tuesday for Archie's parents to consider any other applications they wish to make.
At that hearing, Sir Andrew said: "In short, his system, his organs and, ultimately, his heart are in the process of closing down."
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