Error handling procedure is falling over internally and then trying to send error messages about itself, thus creating a loop

Error handling procedure is falling over internally and then trying to send error messages about itself, thus creating a loop, what can be done with the sender address or not to get this many alerts?

The error message we get is as follows:

{
“logid”: 1566
“PipelineRunTimeId”:
“”
“PipelineRunTime”:
“2020-03-23T18:05:23.903”
“payload”:
“hostname , pipeline name ,$= {error=Cannot deliver the message, reason=Message caused too many failures, resolution=Redirecting message that has caused too many failure to the error pipeline: {}, status_code=too-many-pipeline-failures, original={task_name=…”
“Status”:
“organization_ERROR_”
“ResponseMessage”:
null
}
It is the error that the message could not be delivered ({error=Cannot deliver the message, reason=Message caused too many failures, resolution=Redirecting message that has caused too many failure to the error pipeline: )

After we experience a failure these messages were what the email sender was replaying nonstop.
Eventually the monitor email address gets flagged for excessive mails, and end up been blocked.