We do recommend that parents send a test email to "firstname.lastname@example.org". That will help ensure emails are delivered for some mail providers.
You can check the delivery status for a daily report by going onto the dashboard. Switch over to daily reports and change the date to yesterday. Then click on the child in question. Below their daily report will be a delivery history.
If you provide us with the email addresses that are having issues we can trace them. Sometimes parents accidentally mark an email as spam which prevents us from sending them an email. We can unblock those when requested.