Hello I have been running a low carb website for sometime (as well as being on one myself) so I do have a lot of experience in that area. Firstly fat is very important in a low carb diet, by cutting both you encourage too rapid a weight loss which has a lot of risks on its own plus you also are more likely to burn muscle. Muscle is very important to preserve as it helps regulate your metabolism, by losing muscle you will lower your resting metabolism rate (the rate at which you burn calories), if you gain muscle you do the opposite. Plus fat has a lot of benefits which I won't go into here. If you are doing mostly cardio then you are even more likely to be risking your muscle mass and at the amount of gym sessions you are doing I would say it is a guarantee that is what is going on. I am also concerned that you will get dehydrated if you are not already and that your electrolytes might be very out of wack which can result in death if you are not careful. I would visit your doctor and let him do a check up.

Also if you are eating mainly lean protein your calories are most likely very low. I have been doing research lately into very low calorie diets and they are not something that should be done without supervision by an experienced doctor. There are lots of risks for even obese women/men that do not exercise much, I imagine with you breast feeding let alone all that exercise that those risks would be magnified to a much greater degree.

Breast feeding is very demanding nutritionally so dieting during this time is generally not recommended.

Also generally, a low carb diet that is low enough to induce ketosis is not meant for anyone whom is a child (although epileptic kids are treated with them), breastfeeding or pregnant. Dr Atkins himself would only allow the maintenance phase of his diet in those circumstances.

I am not saying low carb is bad obviously as I truly believe in it but I think you do need some when pregnant or lactating, too little carbs can also lower your milk supply. If you like the health benefits of reducing carbohydrates I would recommend you buy the Atkins New Diet Revolution and follow his maintenance phase which is moderate in both carbs and fat and stick with fresh whole foods.

In essence I think you are exercising too much as well as restricting too much and would suggest you visit your doctor.