An excuse for just about anything, basically means "I can do it, but not now".
Ideally to be in recovery mode means that one can't perform an action because they have already done it recently and are still "recovering" from it. Thought to be derived from the term people sometimes use to describe their state after an intense workout when they are supposedly weaker from straining themselves and can justify dismissing a challenge. Because "recovery mode" allows someone to excuse themselves from doing something and make it seem like this was because they do it so much, it is often used by egotistical smartasses and cocky jocks. However it can also be used in a completely irrelevant way, often to great comedic effect.
guy1: "...no way you go to the gym. Look at you, so pinner!"
guy2: "If you think you're so strong, why don't we arm wrestle right now!"
guy1: "Nah, I'm in recovery mode"
guy2: "Sure, ever since the last time when I won!"
teacher: "Marco, why was your essay incomplete?"
student: "I was in recovery mode"