To put in simpler terms, you can't simply "unarchive" an Instagram story. The story you put remains live for 24 hours after which they vanish and go into the archives. What you can do is repost it as a new story or put it in the highlights section.
Instagram doesn't provide an unarchive option for stories. However, if you want to use a story that you had previously posted, you can simply go to the Instagram archives and reshare the post.
