Summary 

When you have the Invoice Receipt email notification enabled and the Invoices are not sent to the customers, please check the state of the Invoices. Posted and Pending (draft) invoices will not be sent with the Invoice Receipt email notification enabled.

Solution 

By default, all the email notifications are triggered by the events that occurred in Chargebee. Pending invoices are draft invoices that need to be closed by the merchant (either auto close or manual close) and they are generated when Metered Billing is enabled.
So the Invoice Receipt email notification will be sent when the pending invoices are closed.

With regard to Posted Invoices, this status is used when you've enabled Payment Terms (Net D) for your recurring invoices. Recurring invoices are marked as Posted immediately after they are generated. They will remain in this state until the due period has been exceeded. The invoice status will change to Payment Due if the due period has been exceeded, and the amount hasn't been paid.

We have a separate email notification for the Invoices in the Posted state.

Please navigate to Settings > Configure Chargebee > Email Notifications > Payment Terms (Net D) and enable the notification. Please note that you can also send reminder notifications to be sent X days before the Invoice moves to the “Payment Due” state from the “Posted” state, to remind the customers to make the payment.