I'm writing not as a user but as a service provider.
Some of our customers are using Zendesk Support and have voice services with us.
If they set up to send all voicemail notifications to their Zendesk address, our bounce mailbox gets auto-responses to this and tries to determine if the mail is undeliverable.
This might be a configuration problem by the customer, but since we get those mails from more and more different customers, I suspect a general problem in Zendesk or at least a problem in the default configuration.
Our mails have mail headers to indicate to not to send auto-responses:
X-Auto-Response-Suppress: OOF, DR, RN, NRN, AutoReply
These are seemingly ignored by Zendesk, although the auto-responses sent out by Zendesk carry the (more or less) same headers to shut up other autoresponder systems:
Auto-Submitted: auto-generated X-Auto-Response-Suppress: All X-Mailer: Zendesk Mailer
So: Please make Zendesk behave as you expect others to behave and suppress auto-reply mails to those who don't want to receive them.