The phrase "made a run at" is commonly used to describe making an attempt or trying one's luck at something. Antonyms for this phrase could include "avoided," "abstained," "declined," "refused," or "resisted." These words imply a conscious decision to not pursue a certain course of action, as opposed to making an active effort to achieve something. Alternatively, antonyms could also include "fell short," "lost," or "failed," which suggest an unsuccessful attempt or an inability to accomplish a goal. As with any language, context is important when choosing the appropriate words to convey a specific meaning or intention.