Why are out-of-office replies not appearing in the suspended ticket queue?
Many email providers are moving away from the use of out-of-office replies or restricting the domains and organizations to which they will use them to respond. This is in large part because these replies can be dangerous and represent a significant threat of creating an email loop. Not all email systems add the headers that announce the out-of-office response as being automated in nature, creating the potential of an email loop.
Gmail, for example, doesn't send out-of-office replies to Zendesk, because they recognize Zendesk as an automated sender of traffic. As part of responsible sending policies, Zendesk announces itself as an automated system that generates automated traffic. The example headers below help the recipient server to decide what it should and should not do.
For example, you can send out a single email and CC a Zendesk support address to a Gmail user that has out-of-office replies enabled. But you will not see their out-of-office response and it may never arrive in your queue or your suspended tickets view. Because you received it in your external email, it seems that the Zendesk account should have also received it. The behavior can also be intermittent. This is because Gmail is updating its responsiveness based only on what they know at any given time. If they do not know that the CC'd address is attached to Zendesk then they'll send an out-of-office response, as soon as they do recognize the address as being an auto-responder then they will cease.
This is not an issue that Zendesk can solve. This is because a unique email header meant to be used exclusively for out-of-office replies was never established as part of the RFCs that govern automated email behavior.
For more information, see the article: Causes for ticket suspension.