Here is the latest response from WPEngine:
"Apologies for the problems here.
The error message in the log :
[Tue Jul 15 11:13:53 2014] [error] [client 54.88.111.48] PHP Warning: file_put_contents(/nas/wp/www/cluster-2349/learnbonds/wp-content/cache/autoptimize/autoptimize_b1b3a88cd5d8cfd4d1b5a716beef375a.php) [function.file-put-contents]: failed to open stream: Permission denied in /nas/wp/www/common/production/php_prevent_flock.php on line 21
Actually points to the problem.
The WP Engine platform prevents the PHP flock() or the file locking function. This causes an issue with our network attached storage servers and is thus blocked.
Unfortunately, due to the stability issues this causes, we are not able to make exceptions to this currently.
If you are able to reach out to the plugin's developer for an alternative or a way to disable the plugin's built-in caching functionality, that would be most beneficial.
Alternatively, it seems like you might need to find an alternative plugin that suits your needs without the flock() function."