Disable Honeypot on search forms

I have an ongoing problem that the css which hides the hidden field for a form repeatedly fails for anonymous users only, even with css aggregation off.

Clearing block cache fixes the problem, but it returns immediately. Clearing the theme registry does not fix it. I have a feeling it is not happening on Bartik, but hard to be sure on the basis of a few tests, so arguably it is theme issue. It is not happening to other forms on the site. The problem is with the search box on http://www.hiltonbooks.co.uk/full-catalogue-page. It shows up differently in different browsers.