The union asked the U.S. Court of Appeals for the D.C. Circuit to review the rules and the exemption.
In part, they require pilots have 10 hours of rest between duty shifts, with the opportunity for at least eight hours of uninterrupted sleep.
They also regulate the length of a pilot’s workday, depending on when it began.
But the new regulations do not apply to cargo pilots, such as those who fly for Atlanta-based UPS, because the FAA said they would be too costly for carriers to implement.
The Independent Pilots Association said some of the factors the FAA used in determining the new rules are worse for cargo carriers, including night-time flights and traveling across many time zones.
The Airline Pilots Association also expressed disappointment in the cargo exemption.