Antonyms for the phrase "holds one's own" could include "loses ground," "falls behind," or "surrenders." To hold one's own means to maintain a position of strength or equality in a given situation, but the opposite could mean weakening or inferiority. Other antonyms might include "falters," "stumbles," or "struggles," indicating a lack of confidence or ability to maintain a strong position. In a competitive context, antonyms might include "concedes," "submits," or "capitulates," indicating a loss of control or power. Regardless of the specific antonym used, it represents a shift away from strength, resilience, and tenacity.