You were asking about the fat-fast: On the fat-fast, you eat 1000 calories a day for a short period of time (I'll have to look it up, it is either 7 days or 14....). The fat fast is very low carb.... the diet consists of eating extremely HIGH fat -- 90% of your calories should come from fat. Yes really, that is not a typo. The other 100 calories may come from protein or carbs. The fat-fast is designed to get you quickly and efficiently into ketosis. If you haven't lost "x" weight within "y" amount of time, you learn you are metabolically resistant to ketosis, which means that the low-carb diet is going to be very restrictive for you since you will have to be very strict about not eating ANY carbs!
It is an extreme diet. Typically, a person will lose (water) weight very, very quickly. But you CAN'T get enough protein on it, so it is very important that you NOT try to stay on it very long. Its advantage is that it gets you into ketosis quickly. The drawback is that it appears that you lose weight very quickly and most people are very tempted to stay on the fat-fast for too long. Not only can this endanger your health, but since the weight is primarily water, the weight comes right back the minute you stop doing the fat-fast! All that work for nothing!
What I'm trying to say is that the fat-fast does not work well for real weight loss. It is great for some purposes -- getting into ketosis quickly, shedding carbs rapidly if you over-eat carbs for a short period of time (helping you get back on a Low Carb Diet track quickly), and for losing some water right before the "big event" at which you want to look great but absolutely won't be eating or drinking anything....
You'd have to be very serious, really, really committed to low-carbing to want to try doing the fat-fast. Yes, I am trying to discourage you! The only valid reason for you to want to do the fat-fast (at your stage) is to determine if you are metabolically resistant. Frankly, if you are getting the results you reported in your post, you either ARE metabolically resistant OR you are doing Atkins wrong.
I'm not a doctor or nutritionist and I have no idea how your physical condition is influencing your ability to lose weight by low-carbing. I assume you are under the care of a well-informed hormonal specialist....so if I was you, I'd ask my specialist about extreme low-carb diets BEFORE I did anything.
If you are still interested in learning more, contact me on MY SparkPage. I will direct you to my blogs that tell you in more detail what the fat-fast is. And they are more fat-fast favorable; and they give you about 25 "meals" that fit the fat-fast guidelines.
Oh, you'll lose weight; and lose it quickly, but seriously... I have asked repeatedly and no one has EVER claimed to keep off even an ounce of weight lost by fat-fasting.