I have a Script Notes sheet that I use for every page of my blocking script that lists all blocking, costumes, and props. What I do is list the prop on the pages that it is used, then indicate that it is also used in another scene or on another page. I then make a comprehensive props list with all the props in the show, ad then make another props list/breakdown which is broken down by Act/Scene and who carries it on and offstage. For the breakdown, I do list a single prop multiple times by scene. Someone new could be bringing the prop on or off in a different scene, and you must indicate those changes. Therefore, it is helpful to have down every time it is used so that you can indicate these types of things in a breakdown. If you are just making a comprehensive props list for all the props in the show, then listing it just one time is sufficient.