It's definitely not muscle. Muscle takes months or years to build, and can't generally be built to the point you gain weight with it at a calorie deficit. You can improve the quality of your muscle, but not the quantity, at a deficit. To build muscle, you need to eat at a calorie surplus.
Basically, when you work out too much, and eat too little, you slow your metabolism. Your body starts to hold on to the calories you give it, metabolizing it straight to fat, or simply not burning the fat you do have in preparation for starvation. The term is colloquially known as "starvation mode", although that's less than accurate. 1300 might be just fine for you if you weren't working out, but you are... so it's likely not enough.
This thread should help you understand the science behind it: (Scroll down to Coach Dean's response) www.sparkpeople.com/myspark/messageboard.a
Your body needs fuel. 1200-1300 calories is fine for slight women close to their goal weights, and/or who are sedentary, but for those of us who are active, as you seem to be, it simply just may not be enough. Our bodies are pretty amazing, but they're not calculators; I know the math may seem to add up for you, but there are too may variables at play for it to be that simple!
Here's more on why your body needs more to fuel your workouts: www.sparkpeople.com/resource/nutrition_art
Sparkpeople has a great series of articles on Plateau Busting that may be helpful to you: www.sparkpeople.com/resource/fitness_artic
I suggest two things here:
1) Re-evaluate your goals. If you're in the minium safety range Sparkpeople provides of 1200-1550 and you're not very short (under 5'0) or sedentary, you may have set a too-aggressive goal for weight loss. Aim for 1-2 lbs per week... if you're under 200 lbs, then 1 lb per week is much more reasonable and doable. The closer you get to your goal weight, the slower you will lose.
2) Share your food and fitness trackers, and your gender/weight/height. If you take this information and post it up in the diet & nutrition and fitness boards, you'll get better help. Down here, it's more about parenting and family advice. The folks you want to talk to are up in the fitness and nutrition forums. They don't really check down here. :)