Many of the patients who fill the day are bereft, angry, broken. Their experiences are gruesome, their distress lasting and the process of recovery exhausting. The repeated stories of battle and loss can leave the most professional therapist numb or angry. And hanging over it all, for psychiatrists and psychologists in today’s military, is the prospect of their own deployment — of working under fire in Iraq or Afghanistan, where the Pentagon has assigned more therapists to combat units than in previous wars. Major Hasan’s motives are still being investigated. But those who work day in and day out treating the psychological wounds of the country’s warriors say Thursday’s rampage has put a spotlight on the strains of their profession and of the patients they treat.