Are you certain the buff was still active by the time you completed the mission? Many of the day job rewards (including this one) are auto buffs on a limited timer. If you don't complete a mission before the timer on the buff runs out, you get nothing.
I have encountered a variation on this problem where some characters get the inspiration upon dropping a Radio Mission and others don't for the same type mission.
Also the inspirations only drop for combat type missions not FEDEX or Hunts.
Protector Server
Woeful Knight (BS/Regen/Body Scrapper)
Kevin Christian (MC/FF/Primal Controller)
SilverCybernaut (Eng/Dev/Munitions Blaster)
Apixie OhNo (Fire/Fire/Pyre Tanker)
Y'ru Glowen (Rad/Rad/Psy Defender)
The buff was still active, it was displaying in my bar the whole time. Another Day Job buff, the Monitor Duty one, was active, but ran out.
The missions were from Crimson and Unai Keman, a series of instanced combat missions.
According to the description for the Intern day job power (awarded for spending time in Portal Corp) I am supposed to get a large Inspiration at the completion of every mission. This did NOT happen. It appeared that I got a large Inspiration only after the completion of a SOLO mission, or the end of a CHAIN of missions. It definitely did not award one for every mission I completed.