I am very surprised to hear that you are not getting good support regarding this issue, as this is a very common situation and is a routine support inquiry. If you would like, send me your WebID (primary email address for your account) or your Account Number via PM and I will look into that for you.
What you client is encountering is our SMTP quota. There is an article in the DreamHost wiki that explains this, and how it works, in great detail.
Note that even "Press Releases" from your non-profit client must comply with our anti-spam policy, even if you do send them within the limits of the SMTP quota, via Gmail, or any other third party mailer.
--DreamHost Tech Support