The amount of time that users have to re-open a resolved ticket can be set within the User Group permissions. In order to choose this Time Limit, head to Admin > CRM > User Groups > Permissions, and you can choose from a variety of limits all the way from One Day to Forever, and apply different limits to each User Group:
Once this limit has been set, it will come into effect and either allow the users to re-open the ticket if it is within the time frame:
Or remove the ability to re-open the ticket if too much time has passed:
This will also prevent users from emailing in to re-open the ticket, and they will be a sent a rejection email to inform them that the ticket has been rejected, if this email was sent outside of the set time limit.