I requested that Google demote sitelinks for a few pages from one of our sites about 5 or 6 weeks ago, and they've just complied with one of those requests, and the page they've replaced it with isn't great, but it's an improvement.
However, there's something odd about the way Google is linking to the new page from the SERP: they're displaying an old URL that 301 redirects, and displaying a preview of the page that it redirects to -- the sort of thing I've seen when a 302 redirect is in place, but not a 301.
I've checked with our developers, and the redirect has been in place for more than two years. I assume it's been a 301 that whole time, but they didn't specify. It's definitely a 301 now. I can't figure out why Google would keep a redirected URL in their index for so long. I don't think I've ever seen this happen before.
I thought maybe if the old URL had a lot of backlinks it might make some difference, but I've checked in Majestic. The fresh index lists no links, and the historic index has 14, 4 of which are marked as deleted, and none of which were last seen later than the end of 2010.