Thank you for contacting JustAnswer.
I am sorry to hear about the problems you are experiencing in your relationship. The best way to discuss problems and avoid a defensive response from someone is to avoid starting your sentences with "You". Instead you can state, "I feel" or "I want", or "I am confused about". This allows the other person to hear you and to respond to your feelings and concerns. Sometimes people can hear this better through a face to face conversation, but others are more comfortable with a letter that gives them time to consider the issues and respond.
Remember though that you cannot change someone else. If this person has been pushing you away, it may be due to problems in your relationship or problems of his own. If he does not want to have more frequent contact, then you may need to decide if this is the relationship that you want, or if you will choose to end this relationship and find someone who wants what you want.
It is also important to keep in mind that actions speak louder than words. It appears, from you description that his actions seem to indicate that he is not showing you a reason to believe that he is committed to this relationship. Patterns of behavior tend to predict behavior. Unless he shows you reasons to believe that he is putting effort into your relationship (whatever the minimum requirement you may have), I would encourage you to be very careful.
One thing I would add is that it seems that you have been doing quite a bit of emotional work about this relationship. In order for this to be a healthy relationship, we would expect your partner to do a relatively equal amount of emotional work (if you balance it out over time). This may be one way to evaluate if someone is committed to a relationship and to changing in order to make the relationship work. You deserve someone who will put the work into the relationship as well, since it takes two people to make it work. Also, I definitely believe in trusting your gut. It is often a very good indicator of red flags that should not be ignored. Feelings of love tend to be very irrational, while the gut is a good barometer of danger, both physical and emotional. I hope this is helpful and I wish you the best.