Had the same problem out of the blue today as well. I noticed a stuck cron job in my logs and also using a wp-cron manager plugin.
Great cooperation guys 🙂
Thanks Otto for providing the helpful insight and AITpro for the extremely fast involvement!
It’s a .htaccess problem.
It is mostly happening on blogs with BulletProof Security plugin. Even if you deactive it, the “secure .htaccess” file it had created stays in place and fully operational.
To FIX this issue (if you are using BPS) activate the plugin, go to the Security Modes tab, check the red “Default Mode WP Default htaccess File” radio button and click on Activate.