Hello Falko.

If you access this service setting, and you can verify the appointment status is set to "Approved", then the only other thing that could happen is that this service's minimum capacity is above 1, so until the minimum capacity is reached, each new customer comes in as pending.

If that's not the case, please provide me a temporary WP-admin (administrator) user for your site where this happens, so we could log in and take a look ‘from the inside’ as that’s the most efficient way to see and resolve the issue. 

We do not interfere with any data or anything else except for the plugin (in case that’s a production version of the site), and of course, we do not provide login data to third parties. 

You can write credentials here just check PRIVATE Reply so nobody can see them except us.