Men who are non-committal do not usually have a history of particularly long-term relationships. Rather, their relationships will have been months or weeks long, if they had any at all. If a man has this particular relationship history, it would behoove you to ask why. Short relationships indicate a tendency to bail or sabotage when he starts to commit.
Sometimes men who shy away from commitment have a very specific, ideal partner in mind. They do this because it allows them to find fault with the women they date; it is easy for a woman to meet three different criteria, but it is difficult for her to meet 20. So, if you ask a man who his ideal partner is and you receive more than a few bullet points in reply, you should be aware that he may be non-committal.
A non-committal man will clearly state that he is not interested in marriage, having children or other trappings of long-term commitment. If he says he is not interested in these things, you should take him at his word. You're not going to change him over time, and if he says he's not interested in what comes with commitment, then he's probably not interested in commitment itself.
Choosing unavailable women is another sign of a non-committal man. He may, for example, secretly date women who are already in relationships, or he may exclusively date women who are only in town for a short amount of time. Either way, if a man has a tendency to choose women who are not available to him, he is probably doing so to avoid commitment.