Hello,
Your site show the error page, but the response time is still high, so I think there would be an exception that crash your app. If too many person tweet about it, and many people visit, the response time should be lower.
But it's just a guess, can you provide about 100 lines of log (by running heroku logs -t) so that I can state the correct issue please.
Or, you can grant me a temporary access to your log, if you're not familiar with heroku command.
Thanks,