Hi
I do not know what is the exact algorithm of Google CSE admin function when record frequent searches. I could not find real explanation about it on the net. Maybe ask Google about it.
I tried to click on “Learn More” link beside “No queries were sufficiently popular to be listed.” on the page you attached, and find the following explanation there:
“Popular Queries list empty
The most likely explanation is that no query was frequent enough to make it ‘popular.'”
It is a question what means “frequent enough” for Google?
I suppose you had only some query attempts, and it is less than that Google consider as popular query, so it is not displayed in the statistics.
Maybe Google Analytics give you more information about your site if your search field is not used frequently.
Peter