Question

why are isotopes that have relatively short half lives the only ones used in medical diagnostic tests

Answer 1

Radioactivity ionizes cells in the body

Answer 2

 Hence, it is less preferrable to choose an isotope to enter your body, which will emit radioactivity for a long time, so we tend to choose isotopes, the radioactivity of which ceases quickly, so that the least possible amount of damage is caused to the cells