Make sure your leg is securely wrapped around your horse, and make sure your heels are down. Without a good base of support, the top half of your body will tumble down. Make sure your core is tight and you're sitting up straight, and keep your eyes pointed forward. A lot of the time, most riders who have trouble staying in a half seat are lacking the necessary muscle to stay out of the saddle for that long. Work on your leg and core muscles at home, at the barn do lots of no stirrup work, and while you're trying to half seat, maybe only half seat on the long sides and sit around the corners, that way you aren't wearing yourself out as much.