The term "minding store" can be used in different contexts, such as keeping track of inventory, managing a retail establishment, or simply being responsible for a physical location. Antonyms for this phrase might vary depending on the specific application, but they could include ignoring, neglecting, or being absent. In a retail setting, alternatives could be closing up, shutting down, or vacating. In a broader sense, synonyms for minding the store might include overseeing, supervising, or stewarding, which convey a positive sense of responsibility and attentiveness to one's duties.