"connect EMFILE" error in Node.js

I have very recently received a lot of traffic to my site that runs Node.js. With the increasing traffic it has started to crash a lot, which has not happened before. I get the following error in my log:

{ [Error: connect EMFILE] code: 'EMFILE', errno: 'EMFILE', syscall: 'connect' }
Error: connect EMFILE
    at errnoException (net.js:670:11)
    at connect (net.js:548:19)
    at net.js:607:9
    at Array.0 (dns.js:88:18)
    at EventEmitter._tickCallback (node.js:192:40)

Anyone that have an idea why it crash? And ideas how to solve it?

I'm using Express.js and Socket.io. It runs on Ubuntu.