Martha does not mention the war in her letters for several reasons. First, Martha does not agree with the war, and so while she does not mind writing Cross, she does not want to seem as if she is supporting the war by asking questions about Cross's war experience or by seeming concerned about the Americans' actions in Vietnam.
Secondly, Martha is a stereotype of the protesting college student of O'Brien's time. As you probably know, it was not uncommon for college students from 60s and 70s to hold protest rallies and demonstrations or to burn their draft cards. Martha not only represents this group but also the idealist who believes that she can separate the soldier from the war. Many from her time period believed that they could support the soldier but protest the war, but for the soldiers deployed during the war who were already struggling with their own motivation for being in Nam, Martha's attitude often caused more discouragement than encouragement.
O'Brien talks about many things that the soldiers in Vietnam carried. Some of these things are physical, tangible items, and some are emotions, and dreams of home. It is questionable which is the heavier burden.
I believe Martha represents all of the things and people that are outside of the war, to Jimmy Cross. This is why she never refers to the war; she is everything that is not of the war. Cross holds onto his thoughts of Martha as a way of escaping from the awful reality around him.
There is a lot of information on this book here on eNotes; I have attached a link.
Martha epitomizes the alienation that soldiers of the Vietnam War felt, both during and after the war. It was a war that many Americans rejected, and that rejection was exacerbated because it was also the first televised war, bringing its stark horrors into the very living rooms of people who preferred to glorify war at a distance. Martha represents all of us because we, as humans, struggle to connect with people who are thrust into unfamiliar, unfathomable situations. We choose, instead, to gloss over those situations or to avoid them altogether. When Martha's fails to so much as mention the war in her letters, she is grappling with her own discomfort, as well as attempting to preserve her normality. In fairness to her, she may also believe that she is preserving some sense of normality for him by focusing on daily, more frivolous topics. In the process, she only deepens his alienation. This same alienation persisted when the war was over and the men came home to a vague, ambiguous welcome by their countrymen. That detachment from their experience robbed them and us of a healing voice.