A federal district judge rejected Liberty's claims, and a three-judge panel of the Fourth Circuit voted 2-1 that the lawsuit was premature and never dealt with the substance of the school's arguments. The Supreme Court upheld the health-care law in June.
The justices used lawsuits filed by 26 states and the National Federation of Independent Business to uphold the law by a 5-4 vote, then rejected all other pending appeals, including Liberty's.
The school made a new filing with the court over the summer to argue that its claims should be fully evaluated in light of the high court decision. The administration said it did not oppose Liberty's request.
Liberty is challenging both the requirement that most individuals obtain health insurance or pay a penalty, and a separate provision requiring many employers to offer health insurance to their workers.
Liberty law school dean Mathew Staver said, "This case now will go back to the federal court of appeals where we will address the undecided issues that the Supreme Court did not address."
When Liberty's case was in front of the Fourth Circuit, Judge Andre Davis broke with his colleagues who thought the challenge was premature. Davis said of Liberty's claims, "I would further hold that each of appellants' challenges to the act lacks merit."
The appeals court could ask the government and the college for new legal briefs to assess the effect of the Supreme Court ruling.
Also on Monday, the Supreme Court declined to consider whether the Constitution requires states to allow the mentally ill to claim insanity as a defense against criminal charges.
The court gave no reason for turning down a challenge of Idaho's decision not to allow the defense, and three justices objected.
"The law was long recognized that criminal punishment is not appropriate for those who, by reason of insanity, cannot tell right from wrong," wrote Justice Stephen Breyer, joined by Justices Ruth Bader Ginsburg and Sonia Sotomayor.
Four justices are required for the court to accept a case.
The court declined to review the conviction of John Joseph Delling, who had been sentenced to life in prison in Idaho over a 2007 crime spree that left two people dead and one seriously wounded.
Delling, then 21, had become "a type of Jesus," he explained, and the victims were stealing his "energy."
Four states - Idaho, Kansas, Utah, and Montana - do not allow an insanity plea. Delling pleaded guilty to second-degree murder.
Delling's lawyer, Stanford law professor Jeffrey Fisher, contends that Idaho's law violates the Constitution's guarantee of due process of law, as well as the Eighth Amendment's prohibition of cruel and unusual punishment.
This article contains information from the Washington Post.