Tom Evans, 21, and Kate James, 20, had asked Court of Appeal judges to rule that 23-month-old Alfie could go overseas for treatment.
The couple, from Liverpool, have lost cases in the High Court, Court of Appeal, Supreme Court and European Court of Human Rights.
Roger Kiska, legal counsel at Christian Legal Centre, told CBN News last week the parents have the legal right to remove Alfie from Alder Hey Children's Hospital.
But Michael Mylonas QC, representing the hospital, said: "One of the problems of this case is they [Alfie's parents] look at him and, barring the paraphernalia of breathing and feeding, he's a sweet, lovely, normal-looking boy who opens his eyes, [and] will smile".
"Their views and rights do not take precedence and do not give them the choice to make the decisions regarding Alfie", he stated, the news outlet reported.
Justice Moylan also said that the baby's independent guardian has agreed with the hospital that withdrawing ventilation is in the baby's "best interests".
The hearing resumed on 1 February at the High Court in Liverpool, in which lawyers acting for the hospital claimed further treatment for Alfie was futile and inhumane.
Alder Hey Children's Hospital said in a statement: "At each stage of the legal process the courts have agreed with expert advisers... that Alfie's condition is untreatable".
In addition, Moylan said it is "wrong to say that the parents' own views can trump that judicial determination", according to LifeSiteNews. Courts have refused to allow the parents to determine what is in Alfie's best interest. The decision was delivered today at the Court of Justice at about 4:20 PM London time.
In further accusations, Alfie's mother was allegedly asked to leave Alfie's bedside after she questioned hospital visiting rules with supporters, known as Alfie's Army, tweeting on Friday: "Alfie's mummy's been told to leave Alfie's side and removed from the ward for asking the nurse is it acceptable for family members now being told they can not see Alfie". The judge said detail of that plan could not be revealed because Alfie was entitled to privacy at the end of his life. Supporters have since demonstrated outside the hospital and bosses have pleaded with those assembled not to disturb staff or patients.