Running down is a phrasal verb that can have different meanings depending on the context. It can refer to a battery or energy source that is depleting, or it can refer to a physical movement or action such as chasing or pursuing. There are various synonyms that can be used to convey similar meanings to running down. For example, depleting can be used to describe a battery or energy source that is losing power. Pursuing, chasing, or tracking can be used to describe a person or animal running down another. In a figurative sense, synonyms for running down can include criticizing, belittling, or undermining.