You may not be authorizing correctly with the server although ListMail thinks you are.
What you can do is enable advanced SMTP debug messages. Modify admin.php and find the line:
// debug, shows SMTP messages
// $bugs = '1';
change it to
// debug, shows SMTP messages
$bugs = '1';
Then, try another send and see what the server is saying.
You may need to enable the "AUTH" setting and an account's username and pasword to authorize with the SMTP server and/or you may need to enable "Authorize by checking email before sending" with the same account.