There are several synonyms for the phrase "gotten out of my sight." One alternative is "vanished," which suggests that the object or person has disappeared without a trace. Another synonym is "disappeared," which conveys a similar meaning of something or someone being gone or missing. "Lost track of" is another way to express that something or someone has become difficult or impossible to monitor or locate. "Misplaced" suggests that something has been accidentally moved or lost, while "strayed" indicates that something or someone has wandered away from their intended destination or purpose. Finally, "drifted away" indicates a slow and gradual departure from a situation or relationship.