Just as a self reminder, this blog post explains why php-cgi might hang/stop silently when your load increases, and how to fix it, where it explains (in short) that fast-cgi should have the parameter PHP_FCGI_MAX_REQUESTS should equal 1000 or more (this can be done in /etc/default/php-fastcgi on my Ubuntu server).
Also worth a look is this page which has nothing to do with fast-cgi but describes how to increase the timeout in nginx when there is a proxy: http://blogs.agilefaqs.com/2011/07/21/upstream-connection-timed-out-error-in-nginx/ (that is if you get the timed-out connection error and do not find the setting above in the first place). In short:
server {
listen 80;
server_name my.website.com;
server_name_in_redirect off;
port_in_redirect off;
location / {
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Real-Host $host;
proxy_read_timeout 120;
...
}
...
}