London: Archie Battersbee's parents have launched a new attempt to stop their son's life support being turned off.
Archie, 12, has been in a coma since 7 April after being found unconscious by his mother having suffered a catastrophic brain injury at his home in Southend, Essex.
Archie's mother believes he may have been taking part in an online challenge when he became ill. He has never regained consciousness.
His life support was due to be switched off on Tuesday afternoon after the Court of Appeal rejected a bid to postpone the ending of his treatment.
His parents have now appealed to the Supreme Court.
Doctors who are caring for him have said they believe he is brain-stem dead, and argue it is in his best interest for life-support measures to be withdrawn.
The Court of Appeal hearing has ruled that the withdrawal of life support for Archie Battersbee should not be postponed beyond Tuesday.
The government asked judges to urgently consider a request from a UN committee to keep treating the 12-year-old.
But the UN convention on which the request for postponement was based on was "not part of the law of the United Kingdom", the judge said.
The judges also refused to grant permission to appeal against their ruling at the Supreme Court.
However, Archie's parents, Hollie Dance and Paul Battersbee, might now ask Supreme Court justices to consider their application for permission to appeal directly.
In a statement, Ms Dance said she continued to be "shocked and traumatised" by what she feels is "the brutality of the UK courts and the hospital trust".
"Our wishes as parents continue to be trampled on and ignored," she said. "We do not understand the urgency and rush to end life-support.
"The hospital trust has at no point given us time to come to terms with what has happened.
"This is no way for a compassionate society to treat a family in our situation. We will continue to fight for Archie."
Ms Dance also appealed to other parents to ensure their children did not take part in dangerous viral challenges.
Speaking outside court, she said: "Please, please, parents, have the conversation with your children because I know there's a whole new lot of online challenges.