Here's another example of the Google Custom Search disappearing (apparently happened in a new way with FF 4.x)
This site: budgetlightforums.com
should have the Google Custom Search box in the upper left corner of every page.
Under FF 3.x, that disappeared when the NoScript/Advanced/Allow HTTPS Globally ... checkbox got checked
But now, without that checkbox not checked, the Search box isn't shown.
I can navigate directly to the Search for the site: budgetlightforums.com/search
The upper left corner Search box displays -- but doesn't do anything
Instead, using the text entry rectangle under the Google logo on the middle of the page -- searches typed there do work.
Mozilla/5.0 (Macintosh; Intel Mac OS X 10.9; rv:40.0) Gecko/20100101 Firefox/40.0