Archie, 12, is in a comatose state after suffering brain damage.
Three Court of Appeal judges on Monday upheld a ruling by a High Court judge who decided that doctors could lawfully stop treating the youngster.
Archie’s parents, Hollie Dance and Paul Battersbee – who are separated but both live in Southend, Essex, had mounted an appeal bid and argued that Mr Justice Hayden had made errors after High Court hearing.
And they remain determined to keep their son alive, with Ms Dance telling GB News on Monday: "I will fight to get my little boy time."
Their lawyer David Foster said: “Archie’s family are devastated.
Archie Battersbee with his mum Hollie Dance
Supplied
“The family maintain that fair and proper balance was not carried out when looking at Archie’s best interests and will appeal directly to the European Court of Human Rights, or the United Nations, as a result.”
Ms Dance had asked appeal judges to adjourn their ruling.
She said she had seen indications that Archie, who is attached to a ventilator, had twice tried to breathe for himself in the last few days.
Judges were also told that Mr Battersbee had been taken ill outside court before the start of the hearing.
Barrister Edward Devereux QC, who led Archie’s parents’ legal team, told judges that Mr Battersbee, who is in his 50s, had been taken to hospital and was feared to have suffered a heart attack or stroke.
Archie Battersbee
Hollie Dance
But appeal judges Sir Andrew McFarlane, the president of the Family Division of the High Court and most senior family court judge in England and Wales, Lady Justice King and Lord Justice Peter Jackson, said it was in Archie’s best interests that their ruling was delivered as planned.
Mr Foster said Archie’s parents now also intended to “apply back” to Mr Justice Hayden and ask him to review his decision in the light of the “new evidence” about Archie breathing.
Ms Dance added: “We will continue this fight.
“We are discussing options with our lawyers.”
She said she thought appeal judges should have adjourned the ruling once they knew that Mr Battersbee was ill, and added: “I do think it was insensitive.”
Ms Dance said Mr Battersbee was having checks and would stay in hospital overnight.
Mr Justice Hayden delivered a ruling recently after reviewing evidence at a hearing in the Family Division of the High Court in London.
He described what had happened to Archie as a “tragedy of immeasurable dimensions”, but said medical evidence was “compelling and unanimous” and painted a “bleak” picture.
Archie’s parents wanted the appeal court to remit the case to another High Court judge for another hearing.
They complained that Mr Justice Hayden had based his decision on Archie’s “medical best interests”, not his “best interests in the wider sense”.
But Sir Andrew said Archie’s parents’ challenge had no “reasonable prospect” of success.
He explained: “It is clear to me that (Mr Justice Hayden) discharged the important responsibility laid upon him carefully.
“I do not accept there is any prospect of the decision being shown to be wrong or unjust.”
Lady Justice King and Lord Justice Jackson said they agreed.
Judges have heard how Ms Dance found Archie unconscious on April 7.
The youngster has not regained consciousness since.
Doctors treating him at the Royal London Hospital in Whitechapel, east London, think he is brain-stem dead and say continued life-support treatment is not in his best interests.
Bosses at the hospital’s governing trust, Barts Health NHS Trust, had asked for decisions on what medical moves were in Archie’s best interests.
Another High Court judge, Mrs Justice Arbuthnot, initially considered the case and concluded that Archie was dead.
But Court of Appeal judges upheld a challenge by his parents against decisions taken by Mrs Justice Arbuthnot and said the evidence should be reviewed by Mr Justice Hayden.