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I just read through a bunch of the forum posts and have been doing some debugging. My site is hosted on godaddy.com.
What I'm finding is that particular email addresses - especially those that are yahoo.com and gmail.com addresses, are getting filtered by godaddy's relay server. I can't find the pattern as to which addresses are not getting sent and which are, but I have a list of customer email addresses that fail, and others that work with the exact same online form, browser, everything.