The phrase "goes over the hill" implies someone is leaving, running away, or abandoning a situation or responsibility. Thus, its antonyms can be "stays", "remains", "continues", "persists", "endures", "perseveres", or "completes", depending on the context. For instance, if it refers to a soldier fleeing the battlefield, antonyms could be "stays in line" or "fights on". Similarly, if it relates to a teacher leaving the classroom, antonyms could be "stays put" or "teaches continuously". Overall, using the opposite of "goes over the hill" would indicate commitment, determination, responsibility, reliability, and perseverance.