Twitter Search Lets You Once Again Find Old Tweets: " . . . In a post today, Twitter says that some older tweets are now going to be available. How far back? That’s not said; but, it seems like tweets that are particularly popular or notable will be available. From Twitter’s post: As we roll this out over the coming days, the Tweets that you’ll see in search results represent a fairly small percentage of total Tweets ever sent. We look at a variety of types of engagement, like favorites, retweets and clicks, to determine which Tweets to show. . . ."
See also Twitter’s advanced search feature.