An automated "backup" service for your website that crawls around and builds a static copy of all the pages it can see. If the site goes does (or if you push a maintenance mode button) it switches to the static site, maybe with a small warning message. You'd probably need to run the DNS or integrate with DNS services to make that easy to implement. The key is it needs to be stupidly easy to set up.
(ping me if you actually start working on this)