Forum:Book Of Moon vs. Breaker The Magical Warrior

Book Of Moon vs. Breaker The Magical Warrior ok, my question is:

If I have a Breaker The Magical Warrior face up on the field with one counter on him, and my opponent plays Book Of Moon, placing Breaker in face down defense position, does Breaker lose his counter?

the same question applies to Skilled Dark Magician, does he lose his counters when placed in face down defense position?