Stories are only live on the platform for 24 hours. influData can therefore only save a story while it is live and while the creator is being tracked, for example as part of a campaign. Once the 24 hours are over, a story can neither be retrieved nor updated anymore.
For creators tracked in a campaign, influData stores story videos wherever possible. Where a video cannot be stored, the story is kept as a still image instead. That is why some stories in the content overview look like screenshots: you see a snapshot of the story rather than a playable video. Stories that consisted of a single image are shown as images anyway.
Two things follow from the 24-hour limit: stories from a period in which the creator was not yet tracked in your campaign cannot be recovered afterwards, and stories are always shown as up to date on the campaign's Data Status page, because there is nothing left to refresh after they expire (see also "When do changes and new content appear in a campaign?"). The metrics of a story (for example its reach) can still be edited manually in the campaign like those of any other content piece.