Resolved.
There was a problem with apache2 configuration.
The ‘AllowOverride’ was set to ‘None’ for HTTPS version of the site.
I have set it to ‘All’. Now the JSON API is available and JP setting switches are working again.
See also:
http://stackoverflow.com/questions/34670533/wordpress-rest-api-wp-api-404-error
It seems to be a problem with some URL rewrite on my site:
admin.js?ver=4.4.1:9 POST https://grinshow.de/wp-json/jetpack/v4/module/related-posts/active 404 (Not Found)deactivateModule @ admin.js?ver=4.4.1:9(anonymous function)
Similar problem solved here:
https://ww.wp.xz.cn/support/topic/jetpack-cannot-enabledisable-features/
I have the same problem with switching off the ‘related posts’ feature on my site http://grinshow.de
The switch on JP settings page shows ‘xxx has been deactivated’ message, but if I go to other page and return back to JP settings – the switch is still on.