You may think it is your will power that causes your actions. While your will power is important, the real key is your emotion, your feelings.
The fundamental reason of quitting is the lack of emotional involvement. If you want it bad enough, you won't quit. Probably, you don't have a strong emotional drive for losing weight. You don't have a burning desire for losing weight.
Let us imagine the next case. You are told that you would get one million us dollars as a reward if you lose 10 pounds in 3 months. How would you feel? Would you challenge yourself? Probably, you would. Why? Because your emotional involvement has changed. It's much higher than the previous one. Of course, you won't give up, will you?
Your feelings cause your actions. It's worth remembering.