The parents of a terminally ill baby were denied permission to appeal their case to the U.K. Supreme Court in an effort to continue life support for their 22-month-old child.

Kate James and Tom Evans have been fighting in courts to keep their son, Alfie, on a ventilator. But doctors at Liverpool's Alder Hey Hospital said there is nothing they can do for the boy, who is suffering from an undiagnosed degenerative brain disease, and that his life support treatment could stop.

The parents want to continue the treatment for Alfie so that they can eventually take him abroad for treatment.

Last month, High Court Judge Mr. Justice Anthony Hayden ruled that the boy can be moved to palliative care, prompting Evans and James to challenge the decision at the Court of Appeal.

However, the High Court's ruling was upheld and the Supreme Court rejected the parents' claim that the previous courts had discriminated against them.

Court papers revealed that James and Evans wanted to continue treatment so that their son could be taken to a hospital in Rome and perhaps later to a hospital in Munich. The parents vowed to accept withdrawal of life support for the child if there was no prospect of his condition improving after "about six months."

The parents could not simply ask Supreme Court justices to consider the case due to legal rules. They needed to clear an initial hurdle first by convincing the judges that their case was worth arguing.

The three justices expressed "profound sympathy" for the parents, but stated that they had not put forward an arguable case.

"The [supreme court] will give permission for an appeal to be brought only if it would raise an arguable point of law of general public importance," the ruling stated, according to The Guardian.

"The proposed appeal is unarguable so, notwithstanding our profound sympathy for the agonising situation in which they find themselves, we refuse permission for the parents to appeal," it continued.

After the court ruling, Evans revealed that he had asked officials at Alder Hey if he could bring Alfie home to a "suitable setting with the private facilities and team."

He explained that this would allow his son to "die in his own time with no further escalation of treatment," adding that the family would not return to the hospital and would pay for a vent from donations.

The hospital reportedly denied his request, prompting the father to express his frustration on the Alfie's Army Facebook page

"We are being denied this!!!!!" he wrote, referring to his request to take the child home. "Alder Hey want Alfie dead and on their time scale with their plans!!! Whose son is he??? We are absolutely disgusted that our local hospital will not release our son who had every right to live and let live!!!!" he continued.

Evans said that Alder Hey had "failed" his son and vowed to continue fighting alongside James.