I have just upgraded from 3.1 to 3.2, and the search box on the main page reappeared. In 3.1, I had been successfully disabling it by adding this to my xsl (taken from http://dspace.2283337.n4.nabble.com/Remove-search-box-from-main-page-td3283633.html):
<!-- remove search area on home page -->
That is still present in my xsl for my 3.2 installation, but does not suppress the search box.
Seeing that it was failing, I added this to my xsl (taken from https://wiki.duraspace.org/display/DSPACE/TechnicalFaq#TechnicalFaq-HowdoIremovethesearchboxfromthefrontpageinXMLUI%3F):
<xsl:template name="disable_front-page-search" match="dri:div[@id='aspect.discovery.SiteViewer.div.front-page-search']">
This also does not suppress the search box.
I am using a only slightly modified Reference theme, and discovery is not enabled.