I agree with Ducky. I think your calories are pretty low. Try adding a protein shake or something and you could increase your weight training - building muscle buns more calories than the treadmill. Good luck!! Don't get discouraged. The weight will come off
Sometimes adding too much stress on your body will force it to go into storage mode and store.
If you're not already a very small woman, I would suggest double checking your calories. 1200 really isn't that much, so maybe (especially if you're male, extremely overweight, or a tall female) it's not enough calories. I'm 24, 5'5" and at 200lbs/90kgs was told to by Jenny Craig have about 1455 calories until I got down to 80kg/175 lbs and then proceed to 1200. So if you're somewhere between that range of 80-90kgs then maybe try adding an extra (low calorie) snack into your day to see if it helps. Also it's a good idea to spread out your diet, so if you haven't been doing it already, aim for 4-5 "meals" instead of 3 larger meals spaced out very far during the day. Make sure you're drinking enough water too, a good amount of water will help things flow better inside and at the very least give you good bowel movements.
If you're diet is perfect, maybe it's your exercise. Try cutting it back by a day or two. So that you have several days of good exercise with 1-2 days of "rest"- light activity at the most. Maybe your body just needs a rest to remember that no, you're not starving yourself and no, you're not needing all those calories and fat.