e-Newsletter looks like it's sending, but no emails are sent

Everything looks like it's working in e-newsletter. When I go into settings and I test the connection it works. When I go into my wp smtp email plugin and send a test email, it works.

When I create a newsletter, and save it, then send myself a preview, it says it sent but I don't receive it.

The same thing happens if I send the newsletter to myself and the site owner (currently we're the only 2 on the list). When I hit send, it looks like it's working, it says the email got sent, but we don't receive it.

What could be causing this? Gotta get it worked out - thanks!