Not all the domains are showed under Quick Preview in Web Site Preview Settings in Plesk.
The domains are disabled, so DNS service was disabled for the domains as well.
The Quick Preview option lists the domain names which are created by the admin user only.
- Activate the domains on Home > Hosting Services > Domains screen.
- Create domain under administrator or move domain from customer/reseller to administrator and then choose it in Tools & Settings > Web Site Preview Settings > Quick Preview .