When and for what health reasons should we break our fasts? (assume the person is not elderly or pregnant.)
As the other answer mentions, a sick person is not obligated to fast. A regular fast day is a observed as a minhag nowadays, but even on tisha b'av (an actual chiyuv), the basic exemption for sick people still applies. On yom kippur, one may only break the fast if one will be in (life-threatening) danger otherwise. Specific cases should obviously be referred to a rabbi and/or doctor.