Why don't men want to go to doctors? My husband has inability to sustain an erection, and I feel I have to drag him in to be seen. What will happen to him without treatment?

Nothing and alot. Many men are embarrassed and ashamed to have to see a physician. In fact, "nothing" will happen if he is not evaluated, and "everything" can happen - ED is a barometer of an individual's overall health. He could have depression, underlying diabetes or vascular disease, .... If left undx'd/treated these conditions could hurt him in he long term. You could wind up divorced. He should seek help..
It will get worse. Tell him you love him and you miss the intimacy and you are very worried about his health because this can mean there is disease in the blood vessels and heart. Make the appointment for him! try to get him to stop smoking and cut down or cut out alcohol and to exercise. That could help both of you actually.