Antonyms for "keeps one eye on" include "ignores," "neglects," "overlooks," and "disregards." These words suggest a lack of attention or concern toward a particular person, object, or situation. An individual who ignores or neglects something may not realize its potential value or significance. In contrast, keeping one eye on something implies a sense of vigilance and attentiveness, suggesting an active effort to monitor and evaluate a specific situation. While there may be occasions where it is appropriate to ignore or overlook something, maintaining a watchful eye can often lead to increased awareness, safety, and overall success.