By default, an InboundEmail that has been processed will be incinerated after 30 days. The InboundEmail is considered as processed when its status changes to delivered, failed, or bounced.
The actual incineration is done via the IncinerationJob that's scheduled to run after config.action_mailbox.incinerate_after time. This value is set to 30.days by default, but you can change it in your production.rb configuration.
The intention with Action Mailbox processing is that as you process an email, you should extract all the data you need from the email and persist it into domain models in your application. The InboundEmail stays in the system for the configured time to allow for debugging and forensics and then will be deleted.