Twitter Historical data

20 days might be optimistic; their current documentation says:

We also restrict the size of the search index by placing a date limit on the updates we allow you to search. This limit is currently around 1.5 weeks but is dynamic and subject to shrink as the number of tweets per day continues to grow.

There's not a great deal you can do about this at the moment. If you install a tool like The Archivist you can automatically collect and save tweets for future reference, but that won't help with past tweets that have already been and gone. Alternatively you can just take your chances with Google and hope it's indexed the tweets you're looking for.

Hopefully Twitter will eventually relax this restriction and allow searches to go arbitrarily far back in time. They still keep every single tweet, as you can see by paging back through any individual's timeline, but it'll take a significant amount of extra computing power to search through all that data and they probably have other priorities at the moment.

Cheers,

-Tom