Is it possible to add a link in every ticket where you can add the option to send a reminder to the client after the overdue time if the client has not answered within the overdue time?
So maybe add an action or a check box at the ticket status at the bottom called "Remind client after overdue time" or something like this and if you perform this action or tick the box on reply then the client gets a reminder email after the overdue time if she/he has not answered yet.