Instead, they have been given breathing room in the expectation that the U.S. Supreme Court will issue a ruling Monday on a similar fight involving religiously oriented for-profit businesses.
The Third Circuit ordered the archdiocese to evaluate the Supreme Court ruling and then decide early next month whether it wishes to keep fighting its case.
"I'm grateful for the order issued by this [appeals] court, which allows us to continue our pursuit of the First Amendment principle of religious freedom," Archbishop Charles J. Chaput said in a statement. "We will continue on behalf of all believing Catholics to stand up for religious liberty."
The Third Circuit's stay came a day after U.S. District Judge Ronald L. Buckwalter ruled against church officials, who argued that ACA's requirements forced them to sanction contraception coverage, even if it no longer required them to pay for birth control themselves.
An Obama administration compromise, struck in 2012, allows the religious-affiliated nonprofit groups to opt out of paying for birth control - as long as they signed over that responsibility to a third-party health-care plan.
Church lawyers maintained that compromise still "creates a vital link in a chain toward the provision of contraceptive service" and makes it impossible to "adhere to sincerely held Catholic beliefs on the dignity and sanctity of human life."
Buckwalter, however, found the compromise plan did not place a significant burden on their right to religious expression.
His decision landed in a fractured legal landscape on what has become one of the most hotly contested issues in the rollout of President Obama's signature health-care plan.
Nearly 90 cases have been filed across the country challenging contraception mandate as an infringement on religious liberties, according to the ACLU, and courts have varied widely in their opinions. Of those cases, 42 involve religious nonprofits, while 48 have been brought by religiously oriented for-profit companies.
In Pennsylvania, three Pittsburgh-based federal judges have granted exemptions for nonprofits tied to Geneva College, a Reformed Presbyterian school in Beaver Falls, as well as the Catholic Dioceses of Erie and Pittsburgh.
Government lawyers have appealed all three, but the Third Circuit has yet to rule on any of them.
Monday's Supreme Court ruling is expected to settle the matter on the for-profit side of the debate. But since the ACA's rules governing religiously affiliated nonprofits are different from those for for-profit companies, it could leave the archdiocese's question unsettled.
Or the high court could issue a broad ruling that would address the contraception mandate head-on, affecting both the companies that brought the suit - Oklahoma City-based craft chain Hobby Lobby and Lancaster County-based cabinetmaker Conestoga Wood Specialties - as well as all employers who object to the requirement.
As the law stands now, churches are exempt from the mandate. But their nonprofit wings must submit a form to their third-party health plans declaring themselves a religious organization and requesting that they not be charged for contraception use by their covered employees.
Plan administrators then would cover the cost of birth control themselves but could apply for federal reimbursement.
Chaput remained unsatisfied with that solution in a statement issued before the Third Circuit's ruling.
"We will be forced to choose between violating our deeply held religious beliefs," he said, "or grave financial distress that threatens our ability to continue to perform the good works and ministerial outreach to people in need throughout the Philadelphia region."