The Report Sender application sends emails from Salesforce directly, so this means there are only a few areas that can cause issues. Here the are!
Email Deliverability: Sandboxes have email deliverability disabled so that your freshly created sandboxes don't start spamming people by accident. Here's how to turn it back on:
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)!
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.