Let me see if I can describe what I have encountered as clearly as possible.
What I have done is run the recruitment missions that are available and they go into what I assume is a cooldown (the buttons remain greyed out)
Let me preface this with the fact I have NOT verified that a specific elapsed period of time has occurred before clicking again.
I come back to the recruitment officer and all the buttons are greyed out still. Every once in a while I can click on at least the general recruitment button and it will allow me to take the mission, despite the button being grey.
So far I have only encounted this with the general recruitment (that is the top most button correct?)
Again I do not know if the cooldown period has occurred and the button is just not displaying as clickable properly or if I am jumping some queue and getting an early crack at the mission again.