Somewhat ironically, there was a story in the LA Times reviewing the Voice of San Diego, a nonprofit newspaper that specializes in investigative journalism.
Two big factors serve it well: it is nonprofit and it has one very big donor with deep pockets. And yes, it has grants and it's even won a Pullitzer. As the article notes, this may not be THE answer to the future of successful journalism but it is certainly one of the answers. At least there are SOME answers.