Inconsistent permissions behavior

We have several Roles and Groups on our Site.
They used to work just fine.
Now we encounter an odd behavior with our groups permissions, if they want to publish a custom post type.
Sometimes it just works fine, but most of the time it prevents me from uploading a file or publishing the post.

I have not figured out why this is happening.
It seems to me that if i start with the upload it works 90% of the time. When i enter the post title it usually never works to publish the post or upload an image.

Sometimes uploading an image to the post works as intended:

Sometimes it prevents me from uploading a file:

Sometimes it lets me publish the custom post type:

Sometimes it prevents me from publishing a post:

I hope you can help me. I really do not know what todo anymore.
Thank you in advance,
Timothy