Ive written AS as well regarding zero earnings on search lately. They said it was passed on to tech team, will let you know what they say. Guess its not a universal problem or there would be more of us.
Are you using search to allow visitors to search your own site? If so then those clicks may be just that. It could also be that the clicks went to organic search results. I think Adsense only pays when your visitor uses the search box to search the web and then clicks on a paid ad.
I have Adsense for Search on my pages and they contribute about 4% of the total income. That's fine for me. But even if I earnt zero I would still have the search there because it is a simple way for users to locate stuff in my site.
Is there any good reason not to have the Adsense search facility?