So what's the secret to losing a pound a day for many days in a row?
No secret, just lots and lots of sweat. You do eight hours of easy cardio a day. Easy cardio burns (in my case) 600 calories an hour, half of them fat, half of them carbs. To stay out of ketosis, hypoglycemia, and other ugly conditions, you replace the calories you lose in carbs (in my case, 1/2 * 600 calories/hour * 8 hours = 2400 calories), and -- bingo -- you have lost 2400 calories a day (again, in my case) in fat. Together with your basic metabolism and your basic 1000 calorie diet, that gives you a pound a day.
I'm not saying it's healthy, I'm not saying it's realistic for people with a life outside of weight loss, and I'm certainly not recommending it. But it works in theory, it shouldn't kill you, and I think it's how the people on the weight loss shows do it in practice.