Archie was found unconscious at home with a ligature over his head on April 7. His parents believe he may have been taking part in an online challenge that went wrong.
Doctors believe Archie is brain-stem dead and say continued life-support treatment is not in his best interests. Several British courts have agreed.
The family appealed to the U.N. Committee on the Rights of Persons with Disabilities, and wanted the withdrawal of treatment put on hold while the committee examines the case.
“We do not understand what the rush is and why all of our wishes are being denied,” Dance said.
The case is the latest in the U.K. that has pitted the judgment of doctors against the wishes of families. In several cases, including this one, the families have been backed by a religious pressure group, Christian Concern.
Under British law, it is common for courts to intervene when parents and doctors disagree on the treatment of a child. In such cases, the rights of the child take primacy over the parents’ right to decide what’s best for their offspring.
On Monday, the Court of Appeal said that "every day that (Archie) continues to be given life-sustaining treatment is contrary to his best interests and, so, a stay, even for a short time, is against his best interests.”
A panel of three Supreme Court judges said it could only overturn that ruling “if it is satisfied that the Court of Appeal has made an error of law or principle." It said it “is not persuaded that there is an arguable case that the Court of Appeal has so erred.”
“The panel reaches this conclusion with a heavy heart and wishes to extend its deep sympathy to Archie’s parents at this very sad time,” the court said.