Vimcasts.org runs on Radiant CMS, which has page caching enabled by default. My problem was too many app instances spinning up. I've limited the PassengerMaxPoolSize and PassengerMaxInstancesPerApp both to 2, which seems to have fixed it.
I appreciate this burst of traffic to help me get to the bottom of this.
I wonder why you're running a clean site like vimcasts.org on a full-blown CMS. Imho this scenario longs for simpler solutions. Static site generators - in the Ruby universe: toto, nanoc, webby - come to mind.
Well, I guess your passenger/apache is not configured right to deliver the generated static files without using ruby or passenger besides your MaxInstances/PoolSize options.
I remember some issues with passengers and page caching (on nginx e.g.) which needed some tweaks.