How can I maintain the loyalty of my evil minions?

Losing Loyalty

Body bags have an AoE that reduces minion loyalty.
Overwork without recreation reduces loyalty.
Minions with low attention can accidentally trigger traps. This can cause loss of loyalty depending on the trap.

Your avatar has an AoE that inspires loyalty. Make sure you always idle in a well-defended but minion-rich room such as the Control Room.
Loot items have an AoE that increase loyalty. Place these in areas where your minions concentrate (control room, barracks, etc).
Torturing an enemy agent (or another minion) will increase the loyalty of those who witness the act.
Access to a Staff Room with appropriate equipment will keep a minion loyal.
If you see someone deserting, you can capture them and throw them in a cell for a few minutes. They will become very loyal again.
You can execute a minion to make those who witness the act very loyal.