Can I have two transit stays in Beijing, each one less than 72 hours?

I have US passport and will stay in Hong Kong about 3 months for Summer Internship, Hong Kong Training Visa. My flight is as following:
1) flight from US to Beijing and arrive Beijing on May 21, 7:00 PM
2) flight from Beijing to Hong Kong on May 24, 11:00 AM (Will be staying in Beijing less than 72 hours)
3) Flight back from Hong Kong on Aug 8, 9:00 PM, arrive to Beijing 2:00 AM on Aug 9
4) Flight back from Beijing on Aug 10, 2:00 PM to US (will be staying in Beijing less than 48 hours)