If you are seeing a generic message like that on the post edit screen when trying to disconnect posts, that reflects the fact that the ajax request to the server to delete the connection failed, but didn't provide details of why.
There is likely to be more information available in your PHP debug log, can you please check that?
If you haven't already, turn on the debug log by editing your wp-config.php file and change the line with WP_DEBUG like so:
That will create a debug.log file in your /wp-content/ directory which you can examine in any text editor.
Try to disconnect the posts again and then inspect the log.
Please share what you find.
Also, let me ask for credentials to your site, it's likely we'll need to take a look or possibly even take a copy for testing.
I will mark your next reply as private to get log-in credentials from you—you may want to create a temporary admin user for me to use that you can later delete. And be sure to have a current backup of your site.
Can you also confirm in which relationship you are trying to disconnect posts, from which post edit screen?
I can see the issue with the relationship disconnect link on your website, but couldn't reproduce this on my test website.
The duplicator plugin is already installed on your website. Do we have your permission to download a clone/snapshot of the website, to troubleshoot this on our own server?
Thank you for your permission and I managed to deploy your website's clone on my server.
During troubleshooting, I noticed that the IDs stored in the "toolset_associations" table are different than the ones Toolset expects to delete the associations.
Have you performed any bulk import or migration of posts on the website or applied any manual changes to the database? If yes, can you share some details about it?
From the databases, it seems that parent/child posts were changed/re-imported after the post relationships had been imported.
At the moment, there not too many posts involved and I'll recommend to first permenantly delete all existing posts in the "Filmek" and "Események" post types and the "Filmek Események" relationship.