It was a little of all of the above. You might be able to blame part of it on Henry being inbred. But child mortality was quite high during the period - there was good reason that many monarchs have been recorded to have between 4 and over 20 children (cough - Queen Victoria - cough), it is good chance that only half would survive to 13 years old. Hell, Edward barely made it past his teen years. If you made it past your teenage years, expect to live a good and long life up to age 50 to 60 years, 70 and 80 was reserved for royals and people who are darn lucky to live that venerable age.