I just tested after several years "Google custom search" for my site and was shocked.
A search for a key theme of my site brought only 6 results and avoided strictly relevant content.
site:my-site.com key theme
brought 256 results and on the first page, 9 from 10 results had been highly relevant.
Not one page from this 10 "site:my-site.com key theme" results had been listed at Google custom search.
Now I removed all keywords from Google custom search. Hope this helps.