There are a couple of account-level settings related to controlling the email notifications that a captive/embedded recipient will receive automatically from DocuSign. I don't know whether or not these settings affect the "Reminder" email notification for embedded/captive recipients, but it might be worth investigating:

Generally speaking, the "captive/embedded recipient" scenario is designed such that your application will be responsible for communicating with the signer (i.e., by default, DocuSign will not automatically send email notifications to embededded/captive signers, except in cases where the email notification settings above have been set to override this default behavior). So, I wouldn't be surprised if the "Reminder" notification email isn't supported for use with an embedded/captive recipient.
(Added another screenshot -- settings on the Preferences >> Features page):
