It is best to consider the aircraft numbers listed in the firefights as the number of times in the game that you can conduct an airstrike, and each firefight tends to explain specifically the number of times per game.
Airplanes always begin and end their activations off the map.
Once an airplane runs out of APs the airplane is marked as
spent and moves in a straight line off of the map with no altitude or
directional change. Per action, a spent airplane moves the number
of hexes equal to its number of impulses. Moving a spent airplane off
of the map costs the player no APs per action. A player may take no
actions with other units until the spent airplane has exited the map.
Opponents may only pursue and/or fire at the spent airplane while it
An airplane may not re-enter the map if it leaves the map for any
reason, even if it has APs left over. Actions cards may not be played
If you could cite which firefight(s) you are referring to I can tell you more, but basically consider that when a firefight says you get Airplanex X #, the # is the number of times you can have an airplane activate and come onto the board, do its business, and then leave the board, following the rules listed above.
All of the rules quoted were from Section 6.20 In the rulebook, page 16.
Hope that helps!