I am no expert but I have the same problem and in this article
http://blog.sucuri.net/2014/07/malware-infection-breaking-wordpress-sites.html
someone wrote in the comments that it seems that “a newsletter plugin may be the culprit”.
I am also using the plugin MailPoet (Wysija) and after doing a scan with the plugin “WP Antivirus Site Protection” I got following result:
http://screencast.com/t/SW7j917Bb
@smjohnson: Are you using the newsletter plugin MailPoet?