1. You could sell tutorials and ebooks on regexes. People who use your tool might want to understand why their regexes are not working.
2. You could license your debugging code/technology.
3. You could sell a corporate license to use your site. Corps’s regexes won't be shared publicly. Others might be. Corps paranoid about people stealing their regexes might be interested in your product.
4. You could ask for donations to support the site.
5. You could make it social. Have people vote on regexes. Have another complementary site where people contribute test-cases for common regexes like phone numbers, dates, email addresses. You could hold competitions in different categories.
6. You could offer a cloud-based regex parser. I know it sounds a bit absurd, but I want to throw this out there in case it leads to other neat ideas.
7. You could save regexes and have people vote them up. You could have discussion threads around regexes.