Increasing the muscular endurance of your legs means far more than just logging mile after mile of running. While that is exceptional exercise, it is primarily cardiovascular in nature. To improve the muscular endurance of your legs, you need to build strength and improve your tolerance for training volume. Consult a physician before beginning any diet or exercise program.
Run up hills or stairs. This will not only increase your endurance, it will also improve your running technique by teaching you to strike with the forefoot. Increase both your speed and your training volume over time.
Pull a weighted sled. Pull the sled both forward and backward for 50m. Work up to moving twice your body weight, then increase the distance.
Squat deeply for numerous repetitions. Sets of 20 repetition barbell squats will build strength, power and endurance. Never sacrifice good technique for extra weight or a couple of extra reps.
Perform weighted step ups. Hold dumbbells down at your sides and step up onto platforms of various heights. Increase both the weight and repetitions over time.
Jump rope aggressively. Jump for 30 second bursts of speed, followed by 30 seconds of slower recovery time. When you can go for five minutes, decrease the rest period length.