If I may allow myself a guess, possibly the line of thought at livecoding.tv, given the other examples of banned users on your site, and given the lie about the cron job, is that these are merely moronic, worthless customers you're alienating that you wouldn't want on your site anyway. Perhaps you think (thought?) that this is another such instance. This is not the case. You've created a huge leak in your potential enthusiastic user base, which now consists of "programmers willing to stream their content who also happen not to be HN readers."
Mistakes happen. Many startups have survived bad publicity on HN. Your actions have not ensured you a spot in this roster. Even generously overlooking the juvenile behavior of your cofounder and ban messages, the narrative of livecoding.tv stored in the collective brain of HN is now "fails to respond to user and petulantly refuses to apologize for seven hours."
The best thing you can do right now is to identify the responsible individual in your company, apologize specifically, and abjectly, as a company, on behalf of this individual, remove all the ban messages, delete OP's account, explain how a cron job came to enter the story, and both explain and apologize for why this took two hours to resolve after you heard about it.
(Disclaimer: I was about to sign up for livecoding.tv for similar reasons as OP just yesterday. I'm disappointed to know this might've happened to me.)