Antonyms for the phrase "keeps an eye on" include neglects, disregards, ignores, overlooks, and abandons. Neglects is the opposite of keeping an eye on because it implies the act of not paying attention to something. Disregards means to ignore something intentionally or unintentionally. To ignore something is the end result of disregarding it. Overlooks means to fail to notice something. And abandoning something or someone means to leave it behind without a second look. The opposite of keeping an eye on something could also be to lose sight of it, to forget about it or to let it slip your attention.