I am having the same problem. In my case the domain name is entered with a mixture of uppercase and lowercase letters instead of all lower case. Is that also the same with your issue?
The mailbox receives emails fine, but it never replies automatically as it should. Also, did you do any of the following:
I have checked the settings and .qmail and all look fine. I tried it without a mailbox, and with no mailbox and just forwarded (as it was), same issue. I have checked the psa table with: select mn_id, text from mail_resp; to find that the the mn_id is 1141 for this mailbox and then select * from mail where id=1141; and found autoresponder is set to true. I switched auto-reply on and off, no effect. I deleted the mailbox completely and recreated it from scratch and still the auto-reply did not work. I then ran:
/usr/local/psa/admin/sbin/mchk --with-spam
and it all went fine and still the auto-reply did not work. I am sending emails to it from our Yahoo account so these are coming from a totally different network, and I do not get a response. However, if I send an email from the same Yahoo account to other mailboxes on the same server that have auto-reply switched on, all works as it should. This must be a Plesk bug but why is it affecting this mailbox and not the others I tested?