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once you submit a ticket - you should receive an email confirmation. That email is to include a support key (in the body). If an email is sent that includes this support key it is considered a reply to the original ticket.
Make sure that your email templates are setup properly:
/mail_template/ticket_newticket_byemail_notify.tpl
/mail_template/ticket_newresponse_notify.tpl
Both these templates need the following text somewhere in the template:
{TICKET_SUPPORT_KEY}