Judges have dismissed an appeal from the family of a critically ill eight-month-old baby who want to take her for hospital treatment in Italy.
Medics at Nottingham's Queen Medical Centre (QMC) had been told they could withdraw life support for Indi Gregory, who has mitochondrial disease.
A judge denied an application to move Indi to Rome for further care on Thursday.
The family's appeal against the High Court ruling was rejected on Saturday.
Mitochondrial disease prevents cells in the body producing energy and the NHS says the condition is incurable.
Doctors have said Indi is dying, adding her treatment is futile and causes pain.
A High Court judge had allowed medics to withdraw life support, saying the evidence was "unanimous and clear".
Her parents, from Ilkeston, Derbyshire, have failed to persuade Court of Appeal judges in London and judges at the European Court of Human Rights (ECHR) in Strasbourg, France, to overturn the decision to lawfully limit treatment.
On Saturday, Lady Justice King and Lord Justice Peter Jackson rejected their most recent appeal against a ruling to deny Indi the move to Italy.
In their written ruling, the two judges said the appeal would have "no chance of success".
"Indeed we have reached the clear view that after reading all the evidence and arguments that the decision was sadly inevitable and right, and that it was reached with the degree of care that is always appropriate in such a serious matter," they said.
The pair said the judge's decision on Thursday was "not wrong or unfair", concluding there was "no compelling reason" for an appeal hearing.
Indi's parents are being supported by campaign group Christian Concern and its sister organisation, the Christian Legal Centre.
A Christian Concern spokesman said lawyers were considering the next move.