4 reasons your pages to be deindexed by Google

Duplicate content
Even though Google have several videos where they claim duplicate content is not so dangerous for website ranking, it may lead to loosing positions and even disappearing from the SERP.
Blog platforms often show the same content in different pages – monthly archives, label pages and so on. Try to minimize the harm through robots.txt and canonical links.

Penalties
Unprofessional search engine optimization can harm your site and case it to be deindexed from Google. It is better to avoid fast and aggressive methods of link building.

Untrusted site
Thousand pages on the net have some kind of malicious code that harm their visitors. Google tries to ensure its users safety and de-index such pages.
For some reason Google may think that your site is untrusted or even harmful.

Downtime
When SE bots try to crawl your pages and
If your server is down when SE bots try to crawl your pages, they may disappear from the SERP. You can check unreachable pages and other crawl errors through Google Webmaster Tools.