This article covers what is expected behavior when scheduling content to go live a second time after it has been published already.
Once a content item has gone live the first time, this content item can never be scheduled to go live again. A flag is set in the database for published that the go live keys off of. When a content item is published the flag gets set and is not changed back to unpublished even if you archive the content.
The most common scenario seen is someone sets a go live and archive date. Once the content expires they would like to reschedule it again to go live and expect that it will show up on schedule. In order to schedule a content item to go live, a copy of the original item would have to be created.