Whether or not users can re-open a resolved ticket is controlled by this usergroup permission: in Admin > CRM > Usergroups click a usergroup like Everyone or Registered. 

To stop users from re-opening tickets, you can set this permission to off for all your usergroups.

This means that as soon as a ticket is resolved, users can't re-open it.

If you want Users to be able to reopen Tickets for a specific period of time before they are unable to reopen them you can use the settings within this toggle to specify the period of time, such as 1 week.

You can also set the behavior that will occur if a User attempts to reply after the time limit you set.