It sounds like a simple enough plan. Go run for several miles and the fat will melt off no problem. It does work for a while, but you eventually get to a point where it will slow to a halt.
For instance, you have been running 5 miles a day but not losing any weight. What in the world is going on? There are probably several things going on. I knew a guy when I used to work in the gym who would run at least an hour every day, did several marathons, and still carried about 50 extra pounds in his belly. Crazy right?
One major factor is that the more you run, the more efficient you become at it. Great for running, but not so great for fat loss. Your body will get to a point where it burns less calories to do the same amount of work it used to.
Getting to the point where you can run 5 miles was probably a great milestone at one time, but if you keep doing the same mileage in the same amount of time you're not making progress. You need to run farther or run faster. This goes for any exercise you do. If you are doing the same speed, reps, weight, etc... every time you are spinning your wheels. That's the bad part about exercise, you have to keep trying! I know that's tough.
This also leads to another factor and that is overeating. Some runners will assume they can eat and drink whatever they want because they have put in so many miles. If you are still taking in junk calories it will catch up to you. Think about how hard it is to burn off 500 calories running and how quick you can eat or drink 500 calories.
Another contributing factor can be skipping out on your strength training workouts to focus solely on your cardiovascular training. Strength training will not only help keep you injury free, but it will also help tremendously with fat loss.
Strength training workouts will not burn the same amount of calories DURING the exercise session as cardiovascular training, but you will continue to burn calories for hours AFTER your workout is completed. This effect is called the afterburn and there are documented cases of subjects burning calories up to 36 hours after the workout was completed.
Also, the more lean muscle mass your body has on it, the more calories you can burn sitting around watching people on The Biggest Loser be put in coffins. Did you see that by the way? Dude...
While it is possible to lose muscle from doing too much cardio, it has to be an excessive amount to do so. You just need to pick a lane. Are you training to look good or training to be a better runner? You have to be careful if all you are doing is cardio. I speak from experience. I tried it and it made me skinny fat.
When I was running a lot, I got to where I weighed about 185 pounds, which is a good weight but I was a soft 185 pounds. I weigh around 195 now, hardly ever do long distance running, and my body fat is much lower. So I would encourage you to pick a lane!