I notice in statcounter when I've seen that someone has gotten to my site through a search in google that when I click on the link to the search result, I can't find the link to my site in google's search results. It seems when someone clicks through a keyword search result to my site once, google removes my sites for that same search term on subsequent searches. What is google doing to my site? Thanks.
The search results could have changed or it could have been from a different country. If your visitors came from a search in google.com it will not have the same results as from google.se for example. Also, your statscounter may be incorrect.
It's highly unlikely that Google is removing your link. Chances are that traffic is coming from a different Google then the one you're using. For example, you may be using google.com and the result is coming from google.co.uk or another google.something.