After a manual backup can't find the records?

The plugin stores it’s values in 3 places in the WP database: the options table, and 3 tables the plugin creates: participants_database, participants_database_fields and participants_database_groups. If your backup included all tables in the WP database, they will be there, and the plugin will find them. If those tables were not included in the manual backup, you may be lucky and find them in another backup (like a site backup set up in your hosting control panel, for instance).