why i cant lose weight with diet and exercise

Are you not getting results or not getting SCALE results? I went a whole month with no change on the scale when I started a more intense exercise regime, however, I lost inches all over and you can see the difference in the pictures I took.
The scale is one of the least accurate ways to measure your progress. It doesn't measure only the fat loss and a number of things can affect the reading, from the time of day you weight, to the time of month and fluctuations in water weight.
Here is a good explanation of the problems with using a scale alone to measure progress
http://www.myfitnesspal.com/topics/show/350212--why-scales-lie

You may also want to read this article that talks about issues that can arise when we add in lots of cardio and cut way back on calories (if you are only eating 1200 calories and not consuming your exercise calories, your net could be low).
http://www.bodyrecomposition.com/fat-loss/why-big-caloric-deficits-and-lots-of-activity-can-hurt-fat-loss.html

Another thing I would consider if this was me is how accurately I am logging. Are you logging everything, and I mean everything? Are you measuring everything? Are you comparing your labels to MFP options you choose?

ETA- I also wanted to mention - I took my measurements on my waist, hips and bust. My trainer took more but I took those. I saw very little results in those three spots that I measured, however, I lost in my face, my neck, the area between my waist and hips, my arms, my legs.

Great suggestions above - also though may be worth getting some digital scales that measure body fat if you don't already - this may be a better and healthier measure - and show changes a bit quicker than by checking inches lost....

I have run 2 full marathons and 4 half marathons. Every single time I train for a race, I gained weight. Then in between races I'd go on a calorie-restricting diet where I'd lose 10 lbs while exercising less and then go back to my training and gain weight again.

For me it was poor diet. I was eating mostly carbohydrates, because that's what I was told I'm supposed to eat while physically active. Turns out its a lie and that I am slightly insulin resistant (was 20 lbs overweight at my peak).

I was eating 3500-4000 calories during my training weeks, probably 70% carbohydrates. Exercise clearly doesn't help you lose weight if your diet is poor.

Anyways I cut carbs to under 50g/day and I'm 1 month into a marathon training plan. I am eating 2500 calories and more satisfied after meals, losing weight, and am 15 lbs lower than I was at my last race 2 months ago. I have more energy for my runs because I'm no longer burning primarily glucose, but instead burning mostly fat.

Check your diet. Eat mostly fat, then protein, and really lower that carb intake and you will see results. I don't need to restrict calories at all. Its much better regulated by my body now.

You aren't eating enough calories with those hardcore workouts and you are probably in too high of a Heart rate to burn fat and are actually just burning the carbs off of your muscles instead. Guess I learned alot from the New Leaf Metabolism testing I did at my local YMCA!!!! You need to figure out how YOUR body burns fat.

I am pretty sure that it's because you are building muscle and muscle weighs more than fat. The first few weeks are the hardest because you won't see a significant change on the scale, so you think nothing is happening, but really you are getting leaner and more muscular. You may not see a big change for a couple months, but it will happen for sure, it will be worth it. Take measurements and track those instead of the weight. Good luck.

It's not possible to gain muscle on large deficits. If you have a minimal deficit (20% off of TDEE), then it can be possible but not when your 800-1000 calories away from your TDEE

If the OP was under-eating, then she shouldn't have the energy to workout as intensely as she says she is. If she feels energized and not feeling starving on her 1200 calorie diet, then she should be melting off the fat.

There must be more to this story. Maybe she's not doing a good enough job counting the calories and is eating significantly more than 1200 on some days. Just speculating.