We have a node.js server which implements a REST API as a proxy to a central server which has a slightly different, and unfortunately asymmetric REST API.
Our client
It's the limit on number of concurrent connections in the browser:
How many concurrent AJAX (XmlHttpRequest) requests are allowed in popular browsers?
I have upvoted the other answers, as they helped me diagnose the problem. The clue was that node's socket limit was 5, and I was getting 6 at a time. 6 is the limit in Chrome, which is what I was using to test the server.