@Parkins,
Thanks for giving the details. I looked at the system info and it seems WP Cron is enabled.
DISABLE_WP_CRON: Not set
But it seems the amount of memory that is available to WordPress is less, so it is possible that WordPress is running out of memory while trying to delete the posts.
WordPress Memory Limit: 40M
PHP Memory Limit: 256M
Even though 256 MB
is available to PHP only about 40 MB
is available to WordPress.
Add the following line to your wp-config.php
file so that WordPress can get upto 256 MB
of RAM
define( 'WP_MEMORY_LIMIT', '256M' );
More details at http://codex.wordpress.org/Editing_wp-config.php#Increasing_memory_allocated_to_PHP
Let me know if this solves your issue.