The Supreme Court has refused to allow Archie Battersbee's parents more time to take their legal case to the UN Committee on Rights of Persons with Disabilities (UNRPD.)
A stay of execution granted by the Court of Appeal expired at 2:00pm on 28th July.
The family applied for an emergency intervention from the Supreme Court.
However, the deputy president of the Supreme Court, Lord Hodge, Lord Kitchin and Lord Stephens have refused permission.
Archie's mum, Hollie Dance, said: "Words cannot describe how devastated we are. The pressure put on us from the beginning to rush through the process of ending Archie's life has been disgraceful.
"All we have ever asked for is for more time. The urgency from the hospital and the courts is unexplained when other parties have been happy for us to have more time.
"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.
"We will continue fighting for Archie and will not give up."
Lawyers are seeking assurances from the hospital trust that life-support will not be removed while the family make the application to UNCRPD, despite the hospital being now legally able to remove it.
Earlier in the week, the Court of Appeal refused Archie's family permission to appeal a High Court judgment that ruled that the 12-year-old's life-support should be withdrawn against their wishes.