Karwan Ali and Shokhan Namiq, who live in Manchester, had appealed after a High Court judge concluded that four-month-old Midrar was brain stem dead and said doctors could lawfully stop treating him.
But three Court of Appeal judges on Friday dismissed their challenge and declared that their son is dead.
Sir Andrew McFarlane, Lord Justice Patten and Lady Justice King ruled that medics could lawfully “cease to mechanically to ventilate” Midrar.
Mr Ali described the appeal judges’ decision as “terrible”.
She concluded that Midrar was brain stem dead and ruled that life-support treatment could lawfully end.
But Midrar’s parents wanted treatment to continue and had asked appeal judges to overturn Mrs Justice Lieven’s ruling.
Mr Ali said doctors could not be “100% sure” that Midrar was dead and wanted more tests.
He said Midrar was still growing.
The three appeal judges had analysed the case at a Court of Appeal hearing in London on Wednesday.
They concluded that Midrar’s parents did not have an arguable case and declared that Midrar is dead.
Sir Andrew, who is president of the Family Division of the High Court and the most senior family court judge in England and Wales, announced the decision at a further hearing on Friday.
He said evidence showed that “awfully” Midrar no longer has a “brain that is recognisable as such”.
“There is no basis for contemplating that any further tests would result in a different outcome,” he said.
“The factual and medical evidence before (Mrs Justice Lieven) was more than sufficient to justify her findings.”
He added: “No other conclusion was open to Mrs Justice Lieven.”
Mr Ali said after the ruling: “It’s just terrible.”
He added: “I’m just reading what the appeal judges have said, then we’ll discuss it with our lawyers.
“He’s still growing. They can’t be 100% sure he is dead. He’s still growing. His eyes move. I’ve seen them move.”
Solicitor David Foster, who is based at law firm Barlow Robbins and represents Midrar’s parents, said: “The family are disappointed at the decision of the Court of Appeal and are considering an appeal.
“They believe the law in this area should be reviewed and do not consider Midrar’s condition is necessarily ‘irreversible’.”
He added: “They would like to have the court give weight to experts from outside the UK.”
Judges heard that Midrar was born on September 18.
They were told he had been starved of oxygen due to complications at birth, had suffered brain damage, and been placed on a ventilator.
Bosses at St Mary’s Hospital in Manchester had asked Mrs Justice Lieven to rule that ventilation could lawfully be withdrawn but Midrar’s father, who is 35, and mother, 28, objected.
Lawyers representing the hospital’s governing trust, the Manchester University NHS Foundation Trust, said three tests had confirmed brain stem death.
They said doctors had concluded that Midrar was brain stem dead in October.
Appeal judges accepted that evidence.
They declared that Midrar had died at 20.01 on October 1, when he would have been 14 days old.