What prevents organisms from reproducing an unlimited number of offspring?

The primary reason living organisms cannot produce an unlimited number of offspring is senescence, otherwise known as old age.

Cells of the reproductive organs divide and continually make it possible for organisms to reproduce. As time goes on, the old cell dies and new cells replace them through mitotic or meiotic cell division of young cells that still has the ability to divide.

However, as programmed cell deaths occur with old age, the reproductive cells start losing the ability to divide, and when this happens, the ability for organisms to reproduce becomes limited.

More on reproduction can be found here: link

Human Hunting

Natural predators

Old age

diseases