I bought the Military Academy Lvl 1  from the state store and built it.  It is showing under my buildings, but disappeared from the craft and construction page after creation.  Also, when looking at the recipe in the help section, I noticed you need to make a banner to create the building.  I do not have a banner scheme currently.

n1ghtm00n, the buildings that are already constructed do not show in your Craft & Construction tab, you will never need them again.

Banner is required for 2nd and 3rd levels of Military Academy, the first one doesn't need it.