IF you are using workflow publishing and the scheduled publishing, see also this article.
Also, keep in mind that if there was already a published version of the page, then this will be still visible until the schedule of the newly published version.
If I am getting this right, you expect that after you set a new schedule, the page will not be visible on the live site. If this is correct, then you need to un-publish the page first. So, there is no published version available - either through workflow or, setting Publish To date into the past, save the change and then set new schedule date(s) and save again.