Quite honestly, I think SlimShady made some very good points.

1,200 calories a day is not enough for someone who is excersising regularly and/or lifting weights. When the body thinks it's starving it responds by lowering your metabolism to survive and holding on to every ounce of fat for dear life.

12 grams of carb per day is well below induction levels and not enough, either. Cutting below 20 grams a day won't help anyone lose faster but it will get them bored with this WOE very quickly and greatly limits the choices of what is available to eat. It would also leave you rather short in the fiber and vitamin/mineral department.

Bouncing back and forth between less than 20 grams of carb and 50 grams of carb or more may work for weight training (that's not an area I know a lot about), but I don't think most who do it are using that for weight loss. Dr. Atkins also recommends raising your carb levels slowly for a reason. Too big of a carb change can cause an insulin response which is precisely what most are trying to avoid (remember, too much insulin = fat storage) and in someone who is insulin resistant, it doesn't take much of a carb jolt to get that response again. Going from 20 (or 12 in this case) to 50 grams of carb suddenly will likely make you gain a few pounds just from the insulin response and water retention alone and at 50 grams of carb, it's not likely to come off quickly, especially if it wasn't coming off at 12.

All in all, I think Slim's advice was faily sound. Increase the calories, increase the carbs slowly and don't bounce the carb intake up and down trying to break a stall when the first two suggestions will most likely help. I'm not opposed to going back to induction to break a stall, but first you have to be OUT of induction before you can go back to it.