I ran a few traces and see the site is hosted on Rackspace, so I'm assuming it's a shared rental. As for the "Service Unavailable" message, I get this all the time when trying to hit my profile page directly, and sometimes other pages (ie: Waiting for Votes). When hitting specific game score pages, I have no issues, maybe once in a while a unavailable message. My guess is that because my profile page is so heavy with data (I have 80+ scores waiting to be voted through), that the site times out as it's just too much to handle. Either the MySQL db is timing out, or the code to bind that data to the page is timing out the request. These are all assumptions, but I deal with these sort of issues every day at work.
There's fixes for this, short-term caching, sql query tweaks, or maybe take a step back and make the profile page simplier, or even "on-demand" when it comes to viewing waiting votes, latest messages. If it was me, and like Serious don't have the time right now to optimize this web app, I'd just throw more hardware at it, upgrade my hosting package. Easier said than done.
I would be willing to donate a few $$$ to help the site out, and if I was a PHP/MySQL dev, I've volunteer my services to help (I'm a C# guy, developer for 20+ years now).
All in all, this web app was a lot of work for one developer (Serious) to kick out. Let's hope in the near future he can address some of the issues when his time frees up. There has been a # of times where I just give up when trying to access the site and try later... frustrating!