Yes, DoDMERB will request copies of all your medical records from birth to present, regardless of when your asthma was. That is standard protocol for them.
DoDMERB does understand that people move, physicians retire, medical records get lost or destroyed, so if you can not locate some of the medical records, attach a letter to the front of the copies you do have stating what is missing and why (age 4 - 8, moved and can not locate the physician).