no value in sending a letter so don't do it.

You communicated previously to her at one point that you wanted to save the marriage.

She knows.

Writing her a letter re-stating that isn't going to generate any attraction between you & her.

Is there something else at play here?

How was the marriage leading up to the pregnancy?

It seems very unusual that a woman with a 5 month old baby wants to divorce her husband for no reason whatsoever.

Even post partum depression wouldn't explain this.
Her concern would be the pregnancy and her child, why would her depression lead her to divorce you right after having your child?

Is she hiding something from you?

Was she ever unfaithful before the pregnancy & childbirth?

What has caused her to lose attraction for you?

The answer "I don't know????" isn't going to cut it.

Writing a letter will do no good either.

What's the impetus for her divorcing?
What are HER reasons, HER rationalizations?

More info please, you left out 99% of this puzzle.

You have hit on part of your solution in the 2nd last paragraph - moving on or appearing to move on. Perhaps you agreeing with this and possibly appearing to date & see other women will wake her up a bit - just a suggestion.

I will call this problem a game.

And the logic in this game is to do the opposite of what you think you should do.

I feel like writing her a letter to tell her I love her and understand that she doesn't want to be married but I still want to tell her that I want to be married.

Opposite reaction: I'm not going to write a letter, I'm going to get a life and involve my self less with my wife and make myself mysterious.

I feel like calling her and letting her know I think about her and our family and I love her very much and I'm committed to doing anything to save our marriage and create a great life for our family.

Opposite reaction: I'm not going to call her ever. If she needs to speak with me, she can call me and I will keep my responses brief and shorter than her communication to me. I will appear like I'm having the time of my life and that this is actually a great thing for me because i'm going to be single again and I'm going to find someone more worthy of me.

All of this stuff is counter intuitive and yet that's the beauty of it. You don't pursue, you let go of the rope. You don't give her attention, you don't give her any attention. You focus on being a great dad and just be civil with her.

There's my 0.02 cents, speak to Gucci & Puppy, they'll probably tell you something similar.

She doesn't want you because she can have you at any time.
She'll want you when she knows she can't have you and then she'll have to work to get you back.

For your part, rejection sucks and you'll have to find a way of dealing with it and moving on. It's her rejection of you which causes you to pursue her and want to change her mind about you & the marriage. When you stop fighting it and moving on with your life, acting as if, getting a life, 180's and all that hoopla, she will no longer reject you, she won't have to, you will have begun to move on and you won't be pursuing her. And when she stops rejecting you, the dynamic will change because she can't have you anymore and the switch will hopefully be flipped in her that recognizes you aren't a weak wussy excuse for a man and that you will move on and find someone better.

I would still like to know if she had ever seen anyone before the pregnancy or if any infidelity existed before any of this.

Honesty will help here.