There are several reasons why your website may disappear from Google or other web search engine listings, I've included a list of the most common reasons below:
1. Website is inaccessible (continually or at random intervals)
2. Site contains malicious content (viruses, hostile code, etc)
3. Search engine can't navigate the site (no links from one page to another)
4. Taking part in link schemes (linking to lots of other unrelated sites)
1. Site Inaccessible
If you are running into issues with (1)
then you will firstly need to check your code to make sure something isn't causing it to break frequently. If your code is sound then you need to check with your web host to ensure your web server isn't having any stability issues and going offline for periods of time. If you have moved web hosting providers recently then this may also trigger this problem. Simply re-request the search engine to list your site to get back on the listings.
2. Hacked Site
this normally happens because either someone has hacked your site or the web server that holds the site.
Your site may be hacked or defaced through one of several means such as:
You have an old CMS (content management system, i.e. Wordpress or Joomla) that has been breached and maliciously to deface your site. In this case you need to update your CMS immediately. The same can also be true if you have insecure scripts on your site such as upload forms which can be abused if not written correctly.
Your FTP details have been gained by a hostile third party who have used them to upload or modify files on your web hosting. In this situation you need to clean or replace the files they have modified and change your FTP login details to something different and preferably more secure.
If your web hosting provider has been hacked then you will need to contact them for help with this, but this is rare and the more likely cause will be one of the reasons mentioned above.
Once you have cleaned and secured your site, re-request your site to be listed by the relevant search engines. You may also need to follow their de-listing procedure if your website is showing up as an "Attack Site", details on how to do this are normally shown in the attack site warning message.
3. Unable to Navigate
means that you either have dead end pages which don't link to other pages or you have URLs which the search engine doesn't understand (or will ignore). To fix this you need to make sure that your pages link to each other so that the search engines can "follow the thread" so to speak.
If your URLs are unreadable by the search engine then you need to implement a neater URL method. You can do this via .htaccess mod_rewrites on Apache so URLs such as /mypage.php?thing=238&otherthing=29&page=stuff
can be rewritten to /mypage/stuff/
which search engines won't ignore. If you are using a CMS such as Wordpress or Joomla then they normally have a "pretty URL" mode built in which when turned on will do this for you.
Once you have made sure all your pages link correctly you just need to wait for the search engine(s) to re-spider your site, resubmission shouldn't be necessary.
4. Link Spam
normally happens because you take part in some sort of dodgy link distribution scheme to try and boost your search engine rankings by linking to lots of unrelated sites who in turn link back to you. Search engines now detect this sort of behaviour and it will harm your rank or cause your site to disappear entirely. Best to avoid this shady technique, it will only make you look bad.
So hopefully this article has shed some light on why your site may have disappeared from a search engine if it was present previously. Of course there may be some other special reasons but in those instances you are best off contacting the search engine directly to clarify the situation.