Pippa Knight had been in a vegetative state at the Evelina Children’s Hospital in London.
Doctors said life support treatment should be withdrawn, but her mother, Paula Parfitt, said Pippa should leave hospital and wanted specialists to stage a home care trial.
A High Court judge ruled in favour of doctors early this year.
Mr Justice Poole had analysed arguments at a hearing in the Family Division of the High Court in London.
Ms Parfitt, 41, from Strood, Kent, mounted a series of challenges but failed to persuade judges in the Court of Appeal, Supreme Court and European Court of Human Rights to overturn Mr Justice Poole’s ruling.
Mother to appeal after judge said brain-damaged daughter could be allowed to die
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A single mother is preparing to mount an appeal after a High Court judge ruled that her brain-damaged daughter should be allowed to die.
Mr Justice Poole decided earlier this month that specialists treating five-year-old Pippa Knight, who has a rare condition, could lawfully stop providing life-support treatment.
Pippa’s mother, Paula Parfitt, 41, of Strood, Kent, said she was devastated by the decision and was trying to raise money to fund a challenge to the ruling.