Nginx + php fcgi + high load = hang

Supercache generates full cached versions of pages, as well as doing some other internal caching, it's possible there's some sort of timing issue in high-load situations. I'd check your cache folder to make sure it doesn't contain blank files. If it does, you probably have a file locking issue. Solving such an issue may be tricky, and will probably require you to open a bug ticket, as it's likely a problem with the code itself.

I am running a very similar set up (nginx 0.7.61, php+fpm 5.2.10) and my PHP processes never die, even after being idle.

The process control bits of my php-fpm.conf are as follows:

<value name="pm">
    <value name="style">static</value>
    <value name="max_children">3</value>
    <value name="apache_like">
        <value name="StartServers">20</value>
        <value name="MinSpareServers">5</value>
        <value name="MaxSpareServers">35</value>
    </value>
</value>
<value name="request_terminate_timeout">0s</value>
<value name="request_slowlog_timeout">0s</value>
<value name="slowlog">logs/slow.log</value>
<value name="rlimit_files">1024</value>
<value name="rlimit_core">0</value>
<value name="chroot"></value>
<value name="chdir"></value>
<value name="catch_workers_output">yes</value>
<value name="max_requests">500</value>

Note that while I have the apache-like bits defined (they were part of the default config), they aren't used because I have PM style static set.

You can turn up the logs to debug level using this in the global options section:

<value name="log_level">debug</value>

to see if there's a reported reason that it's shutting down workers.

A latch-ditch fix if this doesn't work would be to have a service like pingdom hit a php on your site every x minutes, but my experience with this software combo doesn't suggest that this should be required.