1) A primary reason websites get de-indexed comes when they sell links to other websites. Google does not want websites purchasing links on their site as a way to boost their page rank or search engine position. So, to prevent websites from purchasing links, they will penalize the actual website which sold and displayed the link. So, if you sold text links on your homepage or another popular page of your site - you should consider refunding the money to the advertiser and removing the link.
2) Another reason comes from when you link to bad sites. Every site has a Google Page rank score from 0 to 10. If your website is linking to websites with a page rank score of 0 or 1; then Google can take that as meaning that your website is not high quality. After all - why would a quality site link to a website which Google deems as not being about quality. On the other hand, if your website links to a website with a page rank score of 7 or 8, Google is much less likely to penalize you for that because it is logical that you'd want to introduce your users to a quality site which can offer helpful information. So, overall, be careful who you link to - because if you link to a bad site - it can end up affecting you.
3) Hosting multiple websites on the same hosting account. If you launch multiple websites under the same hosting account - you could end up having all of the websites grouped together off of your core domain. So, the first site you launch, will always host the content of your additional sites. Down the road, this can cause problems, because if one of your websites come into question - then all of your websites can come into question. So if you host multiple sites - it is better to keep them on separate hosting accounts, and if you can't do that, you want to make sure that the only way to access the content on your website is from that specific website. If you can access all of your website content - from one domain - that could cause problems down the road.
4) Duplicate content. It is clear that Google doesn't like duplicate content. And
Google's latest algorithm change addresses this. So, you want to be sure that your content is unique and that it offers value. If your website copies content from other websites - eventually – it probably is going to be hard to find your website in Google.
5) Page extremely slow or not resolving. Google has said that page speed impacts search results. And, if your website goes down a lot - or has periods when the page doesn't resolve - that can have an impact on your website showing up in Google. So make sure your hosting company keeps your website live, and it if it ever goes down - make sure it gets back online as quickly as possible.