Fredo would definitely have done it again. I may be repeating myself here because I don't want to go back and reread what was posted, but I think that, until the boathouse, Michael was willing to believe that Fredo was duped. He innocently talked too much to the wrong people.

But in the boathouse, Michael finally sees that Fredo is MAD. He's angry and resentful of Michael's success. He can't be angry at his father, because he loved Vito too much, but he truly believes that he was capable of taking over the Family, and that Michael was pushed ahead of him. He's FURIOUS at this, and his jealousy would have caused him to try and set Michael up again one day. He was not only envious of Michael's position and power, but his marriage and children, too.

Michael killed Fredo to protect all of his interests, personal and business, since they were intertwined. It was the one sin he committed that he couldn't live with, but it was necessary.