Tom Evans, 21, and Kate James, 20, had asked Court of Appeal judges to rule that 23-month-old Alfie could go overseas for treatment.
The 23-month-old has an undiagnosed degenerative brain condition and has been in care and on ventilation at Alder Hey Children's Hospital in Liverpool since December 2016.
A lawyer representing Tom Evans, 21, and Kate James, 20, on Monday returned to the Court of Appeal to ask judges to rule that Alfie Evans should be allowed to travel to a foreign hospital.
The toddler's family have said they are accompanied by their own doctors, have removed duty of care from the hospital and placed it with their air ambulance, and have a jet ready to take the child to Italy.
The Court of Appeal, the Supreme Court and the European Court of Human Rights upheld that decision.
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The legal battle between Alfie Evans' parents and doctors comes as Alder Hey, one of only four specialist children's hospitals in England, was found to have failed four in five standard checks during an unannounced inspection, The Guardian reported Saturday.
"We're never going to give up on you, Alfie".
In a statement tearfully read outside the hospital on Monday, Alfie Evans' father accused the hospital of "lying to the police", "stripping [Alfie] of his dignity", "taking away the rights of him and his family to be together", and "trying to dictate what is in Alfie's best interests when we have several pieces of evidence showing Alder Hey to be acting contrary to Alfie's best interest", such as "leaving him in poor and squalid conditions.and with moldy tubes".
The judges rejected their application but said that they could go to the Supreme Court to consider the case for a final time.
Protesters gathered outside the hospital last week after a judge endorsed a plan for doctors at Alder Hey to withdraw life support.
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The court stayed the removal of Alfie's life support, pending the decision of the Supreme Court.
The parents lost their bid to allow Alfie to be taken overseas for treatment.
Roger Kiska, legal counsel at Christian Legal Centre, told CBN News last week the parents have the legal right to remove Alfie from Alder Hey Children's Hospital. Moylan argued, however, that both Bambino Gesu staff and staff at Alder Hey agree that no hope remains for curative or preventative treatment for Alfie and that he should receive end of life care.
He is on life support at Liverpool's Alder Hey Children's Hospital which is part of the UK's National Health Service Foundation Trust.
He said medical experts' unanimous view was that Alfie's brain had been eroded by disease and further assessment was pointless. The protests have allegedly caused road blockages and prevented some staff from entering the hospital.
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