The family of brain-damaged Archie Battersbee have been denied permission to take their case to the UN by the Court of Appeal.
Judges upheld a decision by the High Court to withdraw life support treatment for the 12-year-old.
Archie has relied on mechanical ventilation since being admitted to hospital on April 7.
Doctors treating him at the Royal London Hospital in Whitechapel think he is brain-stem dead and say continued life-support treatment is not in his best interests.
Barts Health NHS Trust wants to withdraw treatment and was last week granted permission to follow best interest proceedings in the High Court.
On Monday, appeal judges Sir Andrew McFarlane, the president of the Family Division of the High Court and the most senior family court judge in England and Wales, Lady Justice King and Lord Justice Peter Jackson, on Monday, upheld a ruling by a High Court judge who concluded that doctors could lawfully stop providing life-support treatment to Archie.
A lawyer for his father Paul Battersbee and mother Hollie Dance said they are considering a challenge to the appeal judges’ ruling.
David Foster said the pair, who are separated but both live in Southend, Essex, planned to appeal to the European Court of Human Rights.
Archie’s parents say withdrawing treatment is contrary to the boy’s clearly expressed wishes.
And the family also claims it is in breach of the UK’s obligations under Articles 10 and 12 of the UN Convention on the Rights of People with Disabilities and Article 6 of the UN Convention on the Rights of Children.
These international obligations say states must take all necessary measures to ensure disabled people enjoy equal rights and that governments should do all they can to prevent the deaths of children and young people.
The High Court had found that Archie cannot feel pain and therefore his present treatment regime does not cause him any pain or distress.
Damage to his spinal cord could also prevent his breathing independently regardless of any damage to his brain.
The family’s legal team argues that withdrawing ventilation will therefore result in his certain death.
Judges have heard that Hollie Dance found Archie unconscious with a ligature over his head. She thinks he might have been taking part in an online challenge.
The youngster has not regained consciousness.
Meanwhile, Archie’s father has left hospital after being taken ill shortly before judges ruled that the youngster could be disconnected from a ventilator, a family spokesman has said.
Mr Battersbee, who is in his 50s, was feared to have suffered a heart attack or stroke outside a courtroom at the Royal Courts of Justice in London.
Archie’s family is being supported by a campaign group called the Christian Legal Centre.
A spokesman said on Wednesday that Mr Battersbee had now left hospital.
