Like I said, fail software and administration. If it's the webserver that's overloaded, that's easily fixed with an extra webserver and a load balancer. If it's the database, same goes, although they'd have to duplicate the database. Which shouldn't be a problem, mind.
If they're smart though, they switch to a horizontally scaleable forum software (not sure if that actually exists, mind), and go to a cloud hosting party like Amazon where they can scale on demand, i.e. only pay for what they actually use / need.
Really need to research that though. I actually think a CMS / forum software that works like that could work, and could be sold to bigger websites like that particular one.
Of course, it wouldn't come cheap, so I'm not sure it would even be marketable,
. Perhaps offering it as a service would work out.