The CRM offers you the ability to auto-close inactive tickets for a certain time.
This option is located in Setup->Settings->Cron Job->Tickets, you can enter the time number of hours that must be passed from the last ticket reply in order for the system to auto-close the ticket.
Keep in mind that the system will only auto close tickets with the following statuses: Answered, Open and any other custom statuses you add for tickets in Setup->Support->Ticket Statuses
After the ticket is auto closed, the system will send an email to the customer informing that his ticket is closed, you can navigate to Setup->Email Templates and edit the email template with the name “Auto Close Ticket” to format the contents to fit for your needs, you can even disable this template if you don’t want your customers to be informed when the ticket is auto closed.
Disable Auto Close Tickets
If you want to disable the auto close tickets feature, navigate to Setup->Settings->Cron Job->Tickets and set Auto close ticket after to 0