what is the role of shame in the lives of these soldiers

Many of the soldiers feel guilt or shame for what they did or did not do in the past. Tim originally intended to run away to Canada but lost his courage during a six day stay in a lodge near the border. To Tim, actually making it to Canada and not fighting would have been mor courageous.

In "On the Rainy River," O'Brien tells why he, or should I say why his fictional character actually went to Vietnam. He almost went to Canada instead. His reason for going to Vietnam rather than Canada is not what you think though. What stopped him, ironically, was fear. "All those eyes on me," he writes, "and I couldn't risk the embarrassment. . . . I couldn't endure the mockery, or the disgrace, or the patriotic ridicule. . . . I was a coward. I went to the war."

Obrien considered himself a coward because he WENT to war.