There is no specific setting based on time like that.
There is a way to make it so that tickets which are closed cannot be re-opened. This makes replies to tickets with this status create new tickets.
What I was doing for a while is we created a new Closed status called Closed-NoReOpen. I had a script that checked the database and changed any ticket that was in state Closed to Closed-NoReOpen that ran nightly from Cron (okay so Windows Task Scheduler).
You can create a new status here:
Admin panel -> Manage -> Lists -> Ticket Statuses
On the Item Properties tab uncheck the allow reopen option.
