Here are a few references from NFPA 80-2016:
6.1.3 Operation of Doors. All swinging doors shall be closed and latched at the time of fire.
126.96.36.199 All single doors and active leaves of pairs of doors shall be provided with an active latch bolt that cannot be held in a retracted position as specified in the individual manufacturer's published listings.
188.8.131.52.3 Latching arrangements that do not provide positive latching in the normal mode shall be permitted to be used provided that, in a fire emergency, the door becomes positively latched by means of an automatic fail-safe device that is activated by an automatic fire detector. (See Section 4.7.)
And from the NFPA 80 Handbook:
The term positive latching, as it is used in reference to NFPA 80 and fire door assemblies, has a special meaning over and above the commonly understood definition of the latch bolt simply being engaged in its strike. In the case of NFPA 80 and fire door assemblies, positive latching is required to secure the door leaves in the closed position throughout the duration of the fire door test, which includes the fire hose stream portion of the test after the assembly has been removed from the test furnace. Latching hardware devices for fire door assemblies are designed to withstand the intense heat and stresses that occur during a fire. At some point during the fire, the latching hardware is designed to become fixed (e.g., unretractable), creating a positive latch that will secure the door leaves in the closed position to prevent the spread of deadly smoke, gases, and flames. All of the nationally recognized fire door tests require the fire door assembly test samples to be fully operable before the tests begin, but they specifically do not require fire door assemblies to be operable after exposure to a fire.