Crawling by the Archive team isn't really an option, since the information is mostly personal and private.
However, the way I've addressed this is by making data export part of the story from the start. At anytime, you can request a backup of your stories, and I will send you a beautifully formatted PDF, along with any audio files (and eventually pictures, videos, etc).
If the service ever had to shut down, I'm committed to giving everyone ample notice to download such backups. So worst case, your stories would no longer be accessible at StoryWorth.com, but you would always have them.
Does that seem reasonable? This is something I care a lot about, so I'd love to hear other suggestions.