Inherently this isn't a question, it would be better suited for the r/Battlefield_Live subreddit so the Devs can see it as feedback but eitherway I digress.
It mentioned it was a 6 hour cooldown for me but I haven't played enough to confirm it each time, that said I suppose it's to prevent players from just grinding them out in a few dozen sessions at once and then never touching it again, by spreading it out players will need to return to the operations every now and again in order to get their battlepacks and by extension, the pieces for the two new melee weapon in Operation battlepacks.
I don't know if this system is liable to change, but I would argue more battlepacks before the cooldown triggers at a cost of less time to play the campaign (maybe 5 days) would help with map fatigue a little, that said it's entirely up to DICE.
