There can be many reasons for that:
1. Google penalty.
To check this, login to your Google webmaster account for this website and look for any messages by Google)
2. Duplicate content on the website
To check this, copy 2 lines from the site and paste it in gouge like this "content" . If only 1 search result is found, i.e. ,your website. then it is fine or else duplicate.
3. Over optimisation of exact match keywords
To check, see the back links of the website and the number of links made on anchor text
4. Might be an issue of Honmeymoon period.
To get to know more, email me your website and keywords that were earlier ranking and i will let you know the exact problem.