Restoring an archived video to on-demand (active) status is very simple and can be done by anyone including viewers and content creators.
If you encounter an archived video, it regardless of the video appearing within the context of the Panopto player or simply embedded on a web site, the video frame will appear likely "greyed-out" or "dimmed" with a message indicating that the video has been archived. In the message, there will also be a link to restore the video.
In this screenshot above, this link is titled: "Restore from archive". According to Panopto, the vast majority of videos can be restored in minutes, but in some cases could take several hours. The requestor will be notified when the video is ready to view.