403 Forbidden + Permission Denied - Temporarily?

Im having a strange issue running nginx 1.4.5 and Im hoping someone
might have some ideas.

We have a Symfony based app that we use Capistrano to deploy. The
deploy keeps a few versions of the app around and rotates them off, so
well have two or three sitting out there. The active version is made
active by using a symlink for the document root, so we have something

/var/www/ourapp/current -> /var/www/ourapp/20140721

With current being the document root specified in the server block.

During the push, that symlink is removed and is set to use the new
version. Also as part of that push, a php file is generated to clear
the APC cache for php-fpm, and then called via curl from our
build/deploy server.

For a period of about 2 5 minutes, any calls to this APC cache clear
script or to another db health check script we have fail with a 403 and
the php logs have Permission denied errors. Ive checked the permissions
on the file and on the all of the directories leading up to it and they
are fine. After the 2 5 minutes, it begins working consistently.

We found an article on stack exchange that sounded very similar to our
issue that involved turning off sendfile, however this did not appear to
affect the behavior at all. We do not have any caching turned on.

Does anyone have any idea what could be going on here?