Robert_Charlton - 4:36 am on Aug 31, 2011 (gmt 0)
CalArch - I did some further checking on a site that I know isn't properly canonicalized on the server, but which has been using www for years. That site gets 12 mega sitelinks with or without the www.
That said, I continue to think that you have a canonicalization issue, and perhaps also a predominance of inbound links in the form of http://example.com ...ie, without the www ...or enough of them without www that Google isn't immediately sure how to regard the domain with www.
I don't want to take this discussion off topic by discussing the details of your situation at length here, but if you want to start another thread discussing it, maybe we can look further... and also link to it from here.
(In the new thread, use example.com as your domain. It simplifies lots of things on the forum if you do that.)