In the debug I found this message cURL error 35: Unknown SSL protocol error in connection to http://www.thenewsletterplugin.com:443 (http_request_failed)
I have a list of 69 users and 100 mails per our, but it is about a week sending.
I have done all what is regarding about Cron Jobs from the tips in the Page.
If I sent a test message from Status tab, the page gets blank.
The blank page is clearly a problem. Have you enabled the SMTP? Are you sure the provider has a working mail service for blogs? About the SSL error, where do you see it?