Sorry, I left out a few words. It's three months.

According to filing cabinets and the number of posted bios, this is how many active employees each of you have:

Education: 15
Law Enforcement: 29
Accidents and Catastrophes: 19
Creatures: 46
International Magical Cooperation: 40
Transportation: 24
Games and Sports: 16
Maintenance/Security: 36
Mysteries: 50

To move them to inactive status, it has to be three months or longer since they've posted anywhere in the Ministry of Magic. An employee posting actively in the cafeteria, for instance, but not on their level, is still active. The hope is that they'll eventually become active on their level, too. If you move someone to inactive, just soft delete their bio and move their name to a separate section of the filing cabinet (off the top of my head, I know Cat's filing cabinet is now done that way).