This is explained in the documentation. The index used by the Search API is optimised for recency and only covers the past 7-10 days.
It allows queries against the indices of recent or popular Tweets and behaves similarily to, but not exactly like the Search feature available in Twitter mobile or web clients, such as Twitter.com search.
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Before getting involved, it’s important to know that the Search API is focused on relevance and not completeness. This means that some Tweets and users may be missing from search results.