Update Jun 03, 2016:
As a new update when you try to do this action it gives you an option to whitelist the action in question. Something like this.
Old (outdated ?) story
I am using popular Newspaper theme on few of my websites. While editing theme settings from admin end it suddenly stopped saving theme settings. I tried different thing including inspect element and hence found this in the console. (see admin ajax 403 forbidden message)
Next step was to find what caused it
What was the Work-around?
Is there a permanent or more smarter solution? I don’t know. Disable Wordfence Security,?? NO, not at all!
However here is what I did in order to fix it for me. Look at the image below: