If you can't not find your website on a search engine there could be a few reasons for this including:
- Has the domain name expired?
- Have you paid your bill?
- When a domain expires, it is automatically pushed out of their listings, otherwise they would be full of dead sites !
- Has you website simple been indexed into a new position on a search engine listing
- Look on page two!
- Start advertising your website using Google Adwords
- If your site is "out of date" in terms of content, then a search engine will have ranked it as such and pushed it out of their listings.