OK, so I am replying to my response. I think I have the problem sorted out, but only after contacting DreamHost support. They wrote me back today:
"On Friday, November 5, 2004, at 04:04 PM, DreamHost Customer Support Team wrote:
Autoresponders are only sent once to an email address that is sending a message to a mailbox. This way someone who may write to you daily will not get flooded with autoresponder messages everytime they write you. So the behavior you are listing above is normal."
I was testing with various email addresses and sometimes (probably once a day) I would get a response, sometimes not (probably because I had already tested it with that email address earlier that day.
Solution: set up a catch-all address for one of your domains and use a different email address each time. Should work so that you don't have to wait until tomorrow to recheck your autoresponder.
I suggested that this be included in the knowledge base or some other appropriate place.
Added Note: The support staff at DreamHost is amazing and fast!