It's a kind of joking euphemism. The plain meaning of "robust" is strong, and vigorous, but it can also mean strong and vigorous in a rough or rude way. The speaker wants to say something unpleasant about Mike's agent. He is about to say a plain word. He decides not to say it. "He was very, uh, shall I say..." means "I am about to use a soft substitute in place of the plain word." For example, perhaps Mike's agent is sometimes violent. The speaker doesn't want to say that. He stops to think of a softer word and says "robust."