When you stabilize a dream, you want to make your brain focus completely on the dream experience, while ignoring the body in real life. This is why many stabilization techniques have you concentrate on the sensations occurring in the dream (rubbing hands, spinning, looking around, touching nearby objects, ect.) If you can occupy your brain with the dream experience, you won't start thinking about your real life sensations (pillow on face, laying down). This will help you stay in the dream.

There have been times where I have realized I'm dreaming, and I can still feel which side my real body is laying on. When I focus on this sensation, my brain is focusing on my real body and I wake up. And when people close their eyes, it matches what their real body is sensing so the brain just wakes you up....or so my theory goes.

Moral of the story: if you become lucid, try one of the many classic stabilization techniques. Don't think about your real position in the bed. And if you suddenly start to think about/feel your real body, ignore it and focus on the in-dream sensations by stabilizing. Oh, and don't close your eyes ( this guy has the right idea)