The agency overseeing Medicare was handed a huge loss by an appeals court that found a long-standing agency rule preventing providers from challenging certain factual determinations more than three years old can’t be extended to administrative reimbursement appeals.

The June 29 decision from U.S. Court of Appeals for the District of Columbia Circuit reinstated an administrative appeal in which 277 hospitals claimed a factual error dating to 1983 has reverberated in the years since to depress the amount of compensation...