Yeah we are seeing a few pages go this way but the problem is that no one can say for sure what the cause is so I am reluctant to make any changes. I don't think every example of this has the same "cause" more likely it is a case by case situation, each site has it's own set of issues and as such there might not be a magic bullet.
in matt cutt's blog he says that the main index bot and the supplemental results bot are two different things... its possible that each have a ranking system to determine which page the results go in. maybe it believes that your pages need to go into the supplemental results more than they deserve to go in the main index... so instead of working on things that *should* be on your pages, look for things that *shouldnt* be in your pages. from the sound of it your new website has gone into the supplemental results because it has grown too much too fast. ive heard of SEO experts making sure that upon initial launch a website has a small amount of pages... then after a while the amount of pages that are added are heavily increased.
Links links links, that's the only way I've taken sites out of supps aside from getting rid of Meta Descriptions & Meta Keywords alltogether. I have a Music Blog that was totally supplemental except the homepage, got off my arse & threw 8 PR6 links at the main page & sitemap. Now it's fully indexed
Supplemental results are the never ending story. I got an email from the Google removal console saying that a hundred supplemental pages were removed, and I found that today the count of non-sense results indexed increased rather than decrease