The cron system of wordpress, used by Newsletter, is not a real cron system and probably cannot run correctly every minute. Newsletter set it to run every 5 minutes so probably your provider does not accept a batch of 20 email at once. Your provider should be more friendly and compute an hourly statistcs not a per minute statistic.
There is no real solution for you: you can consider to use an SMTP service like sendgrid.
Stefano.