Loyalty is one of the five character stats in the game.
Minions and Agents aren't robots. This character stat represents their commitment to work. If they suffer too much mistreatment or receive too little inspiration from their leader, they can become dissatisfied with their jobs. If an Agent reaches zero, he will wander around like a tourist until he leaves. If a Minion becomes zero, he will defect from your organization, often stealing from you as he goes.
Minions can recover loyalty simply by observing the Evil Genius perform evil acts. An interrogation, slaying agents, admiring stolen loot, or watching as he or she executes an underling all have positive auras which raise the loyalty stat of your minions. Even being within his or her presence inspires loyalty, as each Evil Genius has a loyalty-boosting aura of varying size and speed.