The dreaded 502 Bad Gateway, nginx + php-fpm

I recently switched to nginx + php-fpm on my server. There are about 60 domains on the server, most low traffic, but some mid-to-high traffic. All seemed to be working fine for the first 12 hours, but then I started getting a 502 Bad Gateway error on one of the high traffic domains. The nginx error log is full of messages like:

The dreaded 502 Bad Gateway, nginx + php-fpm