My home page has a Multi-Node selector for a carousel, the carousel items are created as content items and selected on the homepage.

I have set each carousel item to 'Unpublish' on a certain date to remove it from the carousel on the page. When I look at the item in Umbraco it is shown as unpublished but the item will still appear in the carousel and can still be selected regardless of being published or not. What should I do to remove a content item from the site at a specified date and time?