If you are not receiving your test messages when clicking "Save & Send Test," the most common issue is that the "Approved Sender" email address (from your Marketplaces Settings) and the "Email for Test Messages" are the same in your Account Settings. This can cause issues with certain email clients, and prevent test messages from sending. If this is the case with your account, we suggest changing the "Email for Test Messages" to a different email address you can access, and see if that works. This should allow you to receive your test emails without an issue.
Other troubleshooting tactics we recommend are verifying that these Test messages are not being sent to your spam folder.
Please keep in mind that messages left in "Test" mode will send preview messages to the Sent Messages Summary page under Communications in your left navigation, but these will not send to your email address. Only the "Save & Send Test" one-time test messages will be sent to your email.