Hi Emily,

When a ticket is solved for less than 4 days, it will reopen the ticket once the end-user replies back in the same ticket. If you wish to manage the tickets that reopen when the agent is not available, I suggest that you use the Out of the Office App and integrate it into your Support. The app displays the availability status of the agent assigned to tickets in Zendesk Support. The app prevents tickets from being accidentally assigned to an agent who is unavailable. When this occurs, a pop-up notification is displayed to the agent.

When a pending, on-hold or solve ticket is reopened by an end-user and the assignee is unavailable, a trigger fires that returns the ticket to the unassigned ticket queue.

You may install this app by going into the marketplace or click: https://www.zendesk.com/apps/support/out-of-office/

I hope this helps! Please let me know if you have questions.