Question:

A user replied to a resolved ticket, and got an automatic rejection email from the helpdesk:

Your reply was not accepted because your ticket has already been marked as resolved. Our agents will not read or reply to this message. 

If you would like to create a brand new ticket you can send a new email to support@example.com

Why was this sent? Can I have the helpdesk re-open the ticket instead?

Answer:

The way the helpdesk responds to an email about a resolved ticket depends on the user's permissions.

You can find these settings under Admin > CRM > Usergroups. Then under each user group you can specify how long you would like users to be able to reply to resolved tickets, and what you would like to happen when someone replies.