Archie Battersbee’s life support will start to be withdrawn on Wednesday morning, his mother has said.
The family’s appeal against the decision to end his treatment was refused by the Supreme Court on Tuesday.
Hollie Dance said her son’s treatment would end unless an application was made to the European Court of Human Rights by 09:00 BST on Wednesday.
Archie, 12, was found unconscious at home in Southend, Essex, on 7 April.
He has never regained consciousness and his mother believes he may have been taking part in an online challenge when he suffered brain damage.
Ms Dance said in a statement: “We want to make an urgent application to the European Court of Human Rights (ECHR), but the trust are saying that that has to be submitted at 09:00 BST, which gives us and our lawyers no time to prepare it.”
Archie’s life support will be withdrawn at 11:00 if an application is not submitted to the ECHR in time, she said.
However, the Christian Legal Centre, which has been supporting the legal action by Archie’s parents, said its team would submit an application to the court by 09:00, “in order to give Archie more time“.
Speaking after the Supreme Court’s decision, Ms Dance said she would “fight to the bitter end”.
“I hope I’ve paved the way for any other parents that want to go up against a trust in this country and the justice system,” she said.
Ms Dance said she felt the system to decide treatment options where there is a dispute between families and hospital trusts “needs reforming dramatically”.
Barts NHS Health Trust, which runs the Royal London Hospital in east London where Archie is being treated, said it would continue to “work with the family to prepare for the withdrawal of treatment”.
Court of Appeal judges had previously ruled the 12-year-old’s life-sustaining treatment should not continue beyond 12:00 on Tuesday.
But this was delayed while the Supreme Court heard the application from Archie’s parents.
The family had asked that court 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 it said the Court of Appeal had “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.
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 wished 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.”
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.
Last month specialists told the court they did not believe it was in his best interests to continue treatment.
Alistair Chesser, chief medical officer at Barts Health NHS Trust, said: “Our deepest sympathies remain with Archie’s family.
“As directed by the courts, we will now work with the family to prepare for the withdrawal of treatment.
“We aim to provide the best possible support to everyone at this difficult time.”
The Christian Legal Centre has called for “systematic reform” of the law following Archie’s case.
Chief executive Andrea Williams said: “Legislation must be passed reforming the system. Archie’s case stands in the gap.
“The precedent his case sets can go an incredibly long way to fixing a system which has no room for error.”