I also fall asleep while attempting WILD. Of course there should be practice, practice, practice!
I read in one website that one should observe the sleeping process and shouldn't avoid it. I did it once and it worked. but the next time I felt bad and very bored. Maybe it works for you. In this way, you should be aware of feeling of drowsiness and observe how you slowly fall asleep.then you will find your body sleep and your mind awake.
Good luck