First, check your spam folder in case the message wound up in there by accident.
Make sure the product does not have Enable Templated Email checked with nothing in the Email Message field above that. Our system cannot use a template to generate an email if there is no template provided. :^)
However, if you have done the above deliberately (to disable product-specific emails), and are relying on your Common Thank-you Email to provide a link to the thank-you/download page, that email would not get sent when you "Send free download link", so in that case you should enter a custom message in the field provided whenever you send a free link.