Your not quite giving us enough information. When you say you tried to delete it did it actually delete off of the map? If so when does it reappear, or does it actually not delete when you hit the delete key? If it does delete then reappears the next time you open S&T then it sounds like you might have this POI Pushpin set in your base template. After you've deleted the Pushpin you'll need to Save As... a new template.