As a result I got
"Refused to display 'https://cse.google.com/cse?cx=...' in a frame because it set 'X-Frame-Options' to 'SAMEORIGIN'."
Then I change my ID back to the old one and it's start to work correctly.
Google stop to support iframes for the custom search result. So your old ID's are support iframes, as legacy support but the newly created profiles does not.