I had a similar issue.
I tested by sending to a gmail account. When I verified that job manager was able to send to my gmail account I contacted my web host.
In my case, my client's domain A record was pointing to the web server, but their MX record was pointing elsewhere.
My web host's server was configured to try to send domain email to the web server. When it couldn't find the user it gave up.
I was able to instruct the web server to handle email remotely, but the tech told me to create a dummy email account on the web server anyway. That way the server would not give up before attempting to send it remotely.
This worked on bluehost.com.
Hope this helps someone.