* Google Trust Problems -
There is some debate about this, but there does appear to be a link between loss of Google Trust (or low trust) and Supplemental pages. Websites which develop Google Trust issues or have low trust due to the fact they are new, seem to be more badly affected by Supplemental results than older, more trusted sites with more backlinks from trusted domains.

Google Trust can be lost by linking out to bad neighbourhoods and link farms, or by extensively using reciprocal link directories with 'free-for-all linking' - a strategy which used to improve organic search engine ranking a few years ago, but now has a negative effect, particularly in Google. A website which exists solely on reciprocal links, with few one way links is more likely to suffer loss of Google trust and get more of its page in the Supplemental results, than sites which have attracted quality one way links as an indicator of quality.

The definition of Google Trust -
A complex measurement of website quality and web popularity. It is loosely based on how many backlinks a website has from authority (hub) sites in related field/s.
The definition of Google Trusted sites -

well established websites which often have top 10 Google organic ranking for competitive terms and an established following, being established leaders in their field. For links from trusted sites to benefit your website ranking, they must be related to your website theme.

If you suspect that loss of Google trust has caused Supplemental Results on your website, then re-assess your SEO strategy away from reciprocal linking and concentrate on building quality content to attract more one way links. Also consider removing reciprocal links to non related sites, particularly if you have a 'reciprocal link directory' on your site. Remember that reciprocal linking should not be done to excess - so consider more worthwhile methods of website promotion, such as article writing and submission to decent article sites like Ezine Articles.