Report Sender sends emails from Salesforce directly, so this means there are only a few areas that can cause issues. Here they are!
Email Deliverability: Emails can be disabled in any org, so check this first. Sandboxes have email deliverability disabled by default so that your freshly created sandboxes don't start spamming people by accident. To turn it on, go to Deliverability in the Setup menu and set it to All Email. See Salesforce Help for more.
Bad Email Addresses: Double-check the email address you entered into the recipients' list is correct by copy and pasting it into a new email message in your normal email client. It's uncanny how often people can mistype even their own email address (it happens to us all)!
A Report Failure: If the report schedule is invalid, for example, if the report was deleted, then you should receive an error email instead of the report. If you're using the Send Now link then you should receive an error in the pop-up. These errors need to be resolved, contact us if you need help with any errors.
Email Infrastructure Issues: When you send an email from salesforce, the receiving email server will check a set of common attributes within the email text to ensure the email is valid. The reasons are too numerous to list here, but a very simple way is to use this service to test your email deliverability like https://www.mail-tester.com , just configure one of your simple reports (with no sensitive data) to be sent to the generated email address on that site and they will tell you what issues are in your email configuration. There are a number of Salesforce features that can help with deliverability, we recommend having your admin review the Salesforce help article: Work With Email in Salesforce.
Tip: If you're not sure whether or not a report was even sent, you can get Email Logs from Salesforce to see whether or not the emails are even going out.