Hi Nicolas,
The plugin sets the permissions on that folder accoring to the WordPress settings, which should be a very unrestrictive permission, (0775 or 0777). There might be security feature enabled on your server that automatically changes the permissions if it finds a specific configuration.
The only way to change those permissions is via either FTP, SFTP or via cPanel. I would suggest changing the permission of the uploads/asp_upload/ folder as well as the uploads/asp_upload/style.instances.css file. You might have to try different permission settings before getting the right one. You might have to ask your server provider as well about the correct permissions, as all I can do is only guess.