The primary reason that Atkins type diets lead to stalls, is that the human body isn't designed to run without carbs forever. (for evolutionary reasons)

The thyroid will slow down after about a month with no carb consumption. When this happens, fat loss stops, and you won't make progress in the gym because testosterone (the primary growth hormone) production will slack. You need carb stimulus, in very small amounts, from time to time to prime the pump!. The key is to get that carb/sugar/glucose input at a time when it won't affect insulin levels. If insulin spikes, fat storage is very easy and testosterone is surpressed (you won't heal from your workouts). If you can load carbs without insulin spike, your testosterone stays high, you get an anabolic effect (muscle growth), and you still stay in a low carb (ketogenic state).

How do you do this? Simple. You load sugars WHEN THE BODY CAN STORE THEM IN THE ACTIVE MUSCLE WITHOUT INSULIN, and not convert them to fats and store them as adipose. When a muscle group is active, it can withdraw sugar (glucose) from the bloodstream and use it for energy (or store it as glycogen) without the use of insulin. The cell membranes become "permeable". In that condition, the pancreas does NOT have to secrete insulin, and you get the best of both worlds.

Here's how this is done:
Stay low carb all day as much as possible. When you go to the gym to train, take a bottle (8 oz.) of PURE grape juice (almost 100% glucose) with you. (You can even mix in some egg protein powder with it, because you can use this trick to load branched chained amino acids as well). As soon as you are done lifting, guzzle down the grape juice (with protein powder if you wish) and immediately hit the exercycle for some VERY SLOW cardio. Your active muscle will load the glucose instantly and it will happen without the need for your pancreas to secrete insulin. After about 15 minutes, you can stop pedalling. You will load glucose, restart your thyroid, get an anabolic effect, keep your testosterone levels high and still supress insulin. Afterwards, when all of the glucose is loaded, you will still be in a low-carb ketogenic state and continue to run on fats.