Hey Jip,
I'm glad that you have figured this out, but please let me warn you. The joomla default cache is a mess.
It has a very basic usage - if you have a site that has only articles and you don't have any user interactions than you can use it. But in your case with comments - this is bullshit. When people login on your site, the cache is automatically turned off.
Also if you have cache, then google can't index the comments - as the page that is going to be served is the one with the ajax comments, and not the page that is made for indexing the comments: https://developers.google.com/webmasters/ajax-crawling/

Regards,
Daniel

Hi Daniel,
The problem was caused by Admin Tools Pro. I had to allow the comments component to access the cache folder. Now it works fine.
In the .htaccessmaker of Direct Admin:
Add '/cache/com_comment/' to the field 'Allow direct access, except .php files, to these directories'.

Hi Daniel, thanks for the link. I checked this out, but I do use only conservative caching. Not progressive as mentioned in the 'known issue'. So also with conservative caching on the comments do not work.

https://compojoom.com/support/documentation/ccomment/ch06#id1332049