This question requires a two-part answer.
Part 1: Understanding of how Twitter returns search results.
The results returned from a Twitter search are not as much date limited as they are limited by the number of results.
The size of Twitter’s index fluctuates based on the number of Tweets being made which means, the more Tweets there are, the shorter the index period is. In short, Twitter will return up to the last 1,500 real-time results.
If someone searches for a really popular term such as “Google”, Twitter will return up to 1,500 results — and those results may only go back as far as one hour because the search term is mentioned so frequently. And for a trending topic, the results may only go back 5 minutes.
But a search for tweets from a specific Twitter user (from:username) can also return up to 1,500 results.
The difference is that the results may go back 15 days. This is because Twitter returns the last 1,500 matching results it can find. The less popular the term, or less frequently it’s included in a tweet, the further back in time the results can go.
The end results is; how far back Twitter returns results is dependent of what you’re searching for.
Part 2: Understanding how TweetReports search works.
The most important thing to understand is that TweetReports does not archive all tweets from Twitter. TweetReports only stores tweets from searches made through TweetReports and tweets that are actively monitored (saved as a Tracked Search) by our subscribers. That means TweetReports will retrieve and display real-time results and any matching tweets in our temporary archive that contain your search request — conceivably returning hundreds of thousands or results.