How do you " fail" a mission?

Your chance of success on a mission is determined by your pets stats, so if it's a mission that requires intellect, a pet with high int will have a good chance of succeeding, while a pet with low intellect has a lower chance of success. Sometimes, pets can fail these missions if the required stat isn't high enough.

When you see the missions you'll see they're different difficulty ratings as well, so a pet would have a higher chance of failing a very hard mission over an easy mission.