We have over 10,000 unique visits a day, and averaged out we're serving a page every second throughout the year. But it's not averaged... at peak times we're serving 5 dynamic pages a second.
What this means is that if the queries are slow at peak times, things get queued up. And because the traffic is constant, the queue never gets a chance to be cleared. And the longer the queue gets, the more connections are tied up and the slow the forum becomes.
The server can cope, but the queue just gets too long so everything goes slow. So whilst it can cope it's not ideal.
Just like road traffic. :)