Contacts responding to Closed - Do not reopen incidents

Summary: We have a closed status that does not allow for re-opening the Incident from either a customer or Agent called Closed do not reopen. At closure the Customers get an email telling them we are closing this and to open a new request if additional assistance is needed.

We still have customers replying to the closed do not re-open incidents - so we are never notified of these emails. How do we stop the system from updating a closed - do not reopen incident and creating a new incident

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We want a response to a closed do not reopen incident to open a new incident