A MySQL database was created and still does exist but it is not being listed in the Plesk interface.
This usually happens when the database is not created via Plesk. Instead, it might have been created via SSH.
To get around this, there are two ways :
1. This is the simpler of the two.
Just take a dump of the database.
mysqldump -u <username> -p <password> databasename > databasename.sql
Drop the database.
mysql -u <username> -p <password>
drop database <databasename>
Create the database via Plesk.
Plesk Control Panel >> Domains >> Mysql Database >> Add Database
Restore the database.
mysql databasename < databasename.sql
2. Another method is a bit complex one and is advised for expert users only.
After taking a backup of the current psa database, you will have to edit it from the backend and add the database details in the database table manually.