Sometimes material cost is reduced to promote officers, what triggers that?

The day of the week lets you know what battlefield buff is going on. For instance, at reset

Sunday = Gathering day(No Buff)

Monday = Toy Killing Event(No Buff)

Tuesday = Construction Buff 99% reduction in building materials

Wednesday = Research Buff 99% reduction in research

Thursday = Training Buff (50% off material cost for training)

Friday = Training Buff (50% off material cost for training)

Saturday = Officer day 100% extra on Dummies, Merit Medals, and air force attributes

Also, 50% off on promotion materials which is what you asked about.

There are also little train buffs that do various things like tech points, recruiting signets x5 ect... You can check your in game mail every week to see when and what every buff is. Hope this helps!