The parents of 12-year-old Archie Battersbee have lost their appeal against a court ruling that supports ending treatment.
Archie was found unconscious in his home with a ligature around his neck on 7 April, in what is believed to have been a tragic accident.
He suffered brain injuries and has not regained consciousness since then.
He is being cared for at the Royal London Hospital where doctors want to withdraw life support.
The High Court ruled that it is in Archie's "best interests" to die.
Supported by the Christian Legal Centre (CLC), his parents, Hollie Dance and Paul Battersbee, went to the Court of Appeal last week to challenge this ruling.
Ms Dance has said that her son expressed an interest in Christianity prior to his accident and would not want his life support to be turned off.
Both of Archie's parents believe he should be given more time to recover.
Lawyers for Archie's parents argued that the High Court judgment did not give proper weight to his previously expressed views and religious beliefs.
In the judgment given today, Court of Appeal judges Sir Andrew McFarlane, Lady Justice King and Lord Justice Peter Jackson said that doctors can lawfully end Archie's life support.
Sir Andrew said that medical staff had seen "no signs of life" in Archie and his "every bodily function is now maintained by artificial means", the BBC reports.
He also said that Archie's religious beliefs were "insufficient" to justify the continuation of life support.
Responding to the ruling, Ms Dance said: "All we have asked for from the beginning is for Archie to be given more time and for Archie's wishes and ours to be respected. As long as Archie is alive, I will never give up on him, he is too good to give up on.
"When he is to die, we believe it should be in God's way and in God's time. What is the rush? Why is the hospital and the courts so keen to push this through as fast as possible?
"I don't believe there is anything 'dignified' about planning Archie's death. For me, this would be the most traumatic outcome.
"Parents need support, not pressure. It is exhausting what we have been through. We should not have to endlessly battle the hospital in the courts for what we believe is right for Archie.
"Top judges have told us, however, that this is the law. If this so, the law must change."
The CLC said that the family will now consider their legal options and have a stay of execution until 2pm on Wednesday.
CLC chief executive Andrea Williams said she was disappointed the judges had decided not to delay judgment despite Archie's father being rushed to hospital after falling ill.
"Archie's parents are not unrealistic. They have been forced into a relentless legal fight because they want their critically ill son to have more time and to be given every chance of recovery, no matter how small those chances are," she said.
"There is nothing 'dignified' about a choreographed, planned death at a specific time by removing the life-support of a critically ill child against the wishes of their parents.
"No family should have to endure endless court hearings over the hospital care of their sick children. Parents must be given more say in how their children are treated.
"Families should not have to battle with hospitals over what is right for their own child.
"Following another disappointing ruling in the Court of Appeal today, we would encourage MPs and members of the public to engage with and support 'Charlie's Law' which we pray will prevent more families having to experience what Archie's family has.
"We continue to stand with Archie's family."