Falling asleep
If you fall asleep, don't be concerned. it can be a good sign since it shows that you are relaxing well, though perhaps just a bit too well.
Take several deep breaths, move your body a little and continue practicing. Many people have a good experience after this step.
Take care to also use a little more effort. You may need more concentration. An Image or mantra can be very helpful here. When we look something or listen to something, it's easier to maintain our consciousness. Visualization of an image or recitation of a mantra will maintain your concentration and consciousness continuously.