The autoresponders have two settings that can be applied to them. Here are the descriptions of these settings found within the online help
Disable responses to indirect mail - By selecting this checkbox, the auto-responder will only be triggered by email sent directly to you. Any email you receive through a mailing list, forward, or an alias will not trigger the auto-responder.
Limit responses to once daily - Select this checkbox to ensure an email address only receives the auto-responder message once per day, even if they send you multiple messages. If you disable this option, every email you receive will your auto-responder. It is HIGHLY recommended that you keep this option turned on to avoid the potential of your email address, your domain, or even potentially your entire mail server from becoming blacklisted by an ISP.
Your client can try adjusting these settings to be sure that every email receives the out of office response.
I hope this helps!