Not losing weight :-(

The safest recommended rate to lose is 1 pound/week. So, it seems like you are losing that. If you're eating 1200 calories and also burning 1200 calories, then your net calories are ZERO. That's not good. Your metabolism may have slowed because it thinks you are starving in some wilderness and it doesn't know when it is going to get food again, so it's probably holding onto every blasted calorie it can. My suggestion would be to eat MORE. Don't go crazy and make it healthy calories, but more of them.

Also, make sure you get enough sleep, drink enough water and get enough protein and fiber.

You HAVE to eat what's right for YOU!
Check this out:

Women:
655 + (4.3 x weight in pounds) + (4.7 x height in inches) - (4.7 x age in years)

Men:
66 + (6.3 x weight in pounds) + (12.9 x height in inches) - (6.8 x age in years)

Please note that this formula applies only to adults.

More: Calculating BMR

Calculate Activity

Step two: In order to incorporate activity into your daily caloric needs, do the following calculation:
If you are sedentary : BMR x 20 percent
If you are lightly active: BMR x 30 percent
If you are moderately active (You exercise most days a week.): BMR x 40 percent
If you are very active (You exercise intensely on a daily basis or for prolonged periods.): BMR x 50 percent
If you are extra active (You do hard labor or are in athletic training.): BMR x 60 percent
Add this number to your BMR.

The result of this formula will be the number of calories you can eat every day and maintain your current weight. In order to lose weight, you'll need to take in fewer calories than this result.

As you lose weight, you can re-calculate the formula to assess your new BMR.

Create a Calorie Deficit

In order to lose weight, you must create a calorie deficit. It is easier and healthier to cut back your calorie intake a little bit at a time. Every 3,500 calories is equivalent to one pound.
So, if you cut back 500 calories a day, you should lose about one pound per week. That said, If you exercise to burn off 500 calories a day you should lose approximately one pound per week. Do both, and ... you get the picture. Ideally, you should do a combination of both, (such as cut back 250 calories; burn an extra 250 calories).

Your weight loss will vary from week to week and at times you may even gain a little weight -- if you're working out you could be developing muscle, which weighs more than fat.

The long-term results are what matters.
http://weightloss.about.com/od/eatsmart/a/blcalintake.htm

I know that this is not a popular belief, but I think that doing too much exercise at once (i.e. going from 0 to too much) actually slows your weight loss right down.
I once had a fitness trainer who told my overweight friend that she needs to do about 30 mins of cardio 3 x a week but concentrate on losing weight first before she starts with "serious" workouts. So she went on a diet and did some cardio (on and off) and actually lost weight quickly.

I followed that advice when I started my weight loss program - only did 30 mins of fast walking (I did it daily) and that was it, but I stuck to 1220kcal most days (I had my goal set on losing 1.5. pounds a week, now I upped that to 1 pound a week, because it is hard sustaining 1220kcal diet for longer periods of time)

Good luck.

Try something other than the scale to track your progress. With all that gym work, you're probably reshaping your body composition and that may take a while to show on the scale, discouraging you. Of course, even with measurements, it could take 6 weeks to see a noticeable difference and it sounds like you're already having trouble with patience with regard to weight loss. It's hard to realize that this is a long term process. Like others, I think your weight loss rate sounds pretty good. 4 lbs in one month is a very decent rate. You might need to adjust your expectations.

Great advise here, it pays to eat more, sounds strange but true. Hang in there.