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.