Notifications Emails Not Delivered By Email Delivery System

Email Delivery System at TMD Hosting blocking out going mail notifications on batches of 10 over a 10 min window. I am sure it has something to do with the site being moved to another server using different DNS servers over a week ago that was needed to run a specific app. Tech support has been struggling to get it fixed for days now.

Email to receive critical site notifications is receiving mail ok, but the Email to send site messages from is getting blocked and bounced back with email message:

This message was created automatically by mail delivery software.

A message that you sent could not be delivered to one or more of its

recipients. This is a permanent error. The following address(es) failed:

  xxxxxx@gmail.com

   Domain xxxxxxx.com has exceeded the max defers and failures per hour (40/5 (50%)) allowed. Message discarded.

Even a batch of 10 over a 10 minute time with known good addresses is shutting down the mail system for 30 minuets with 6 hours between batches. Host has yet informed me on what is causing the failures. The largest batch observed is 46 in 12 minutes and does not seem to many. I look for a quota x/minute and can not find any settings in c-panel setting limits.

Has any one else had a similar problem and what was the solution?