There is a bug in Google that is wiping out search feature that allows searchers to search within a specific site from the Google search result snippets. The feature launched three years ago, and it is officially called a Sitelinks Searchbox. In the Searchbox, Google shows a search box directly within a search result snippet, allowing the searcher to restrict their search results to pages within the site listed.
The following screen shots by Barry Schwartz shows what it looks like on a search for “YouTube” when the feature launched.
The Sitelink Searchbox, at least temporarily is no longer showing. RankRanger caught the feature dropping out of Google globally a few days ago.
At the time of this writing, Google is working on it with no estimated fix timeline.