Just went down again. No indication of any errors or warnings in the php-fpm logs. Nginx just logged:

2013/11/18 19:31:25 [error] 25219#0: *1612 recv() failed (104: Connection reset by peer) while reading response header from upstream

I just implemented the following /etc/sysctl.conf

fs.file-max = 65536

Then ran:

sysctl -p && service php-fpm restart

We shall wait and see if that helps.