The reason for my asking whether you were on an Exchange Server is this, per Outlook Help: "The Out of Office Assistant command does not appear unless you are using an Exchange Server e-mail account and you are in the Mail view." So, I have no idea how you could have set up such an automated reply.
In your original post, you said, "Some time ago, I was experimenting to see if I could set up such a message ...". Did this Outlook behavior start at that time or not?
Edit: OK, I just saw your last post. Glad to hear problem resolved.