Question

Why did people not live past age 40 during the Middle Ages?

Answer 1

A major reason we live so long today is due to improvements in medicine. So you can probably infer that disease killed many people before their 40th birthday. You could probably also attribute short life spans to war as well.

Answer 2

Just adding to jedi_trooper's answer (which I agree with), sanitary conditions were also pretty abysmal contributing to disease and health issues. No toilets, no general plumbing, just a pot to do your business in which was emptied out the nearest window. Bathing back then was a thing most people did once in awhile, like once every few days or weeks.