Could a superhero be liable for taking a day off?

It is a well known principle of tort law that, as a general proposition and subject to only a few exceptions, there is no duty to rescue. But should this principle apply in the case of a superhero like Superman or Batman who have, or at least it seems they have, imposed on themselves a duty to help those in need? This oddly interesting question is the subject of a recent entry in a blog dedicated to discuss legal issues surrounding the lives of superheroes and supervillains called Law and the Multiverse.