I have a site on a shared host. I have few visitors. Almost daily I notice times when my site is down err 500. I check that I used 100% CPU and/or RAM at these times. The site dies for 10-15min then returns to normal. Host won't give me any logs, so I can't say if it's the same times.
Since there aren't that many visitors, the possible plugins responsible are WordPress Backup to Dropbox or Better WP Security. Today WordPress Backup to Dropbox failed and wasn't backing up and I still had the 100% CPU and downtime.
My host keeps saying optimize something, of course without any other info. They said I should disable wp_cron. I searched and the best info link was
http://wp.tutsplus.com/articles/insights-into-wp-cron-an-introduction-to-scheduling-tasks-in-wordpress/
It doesn't sound like I should disable wp_cron.