With an estimated 175 million Twitter users, it’s no wonder it’s so hard to track down old tweets—yours or anyone else’s. Twitter stores them forever, but because of capacity limitations, its search engine takes you back just a week or two. Your only other option is to manually scroll through the individual tweets on a page, which is inefficient and does you no good beyond the 3,200-tweet limit.
If you need to search back further, start with TweetScan, which keeps an index to 2007; though incomplete, it’s often the best bet. If that doesn’t work, you may still be able to retrieve what you need using a search engine. Try Googling with a query like this: twitter.com/username keyword (swap in the username of the person who tweeted and a keyword from the tweet).
For easier access to your tweets in the future, back them up. Among the services available, TweetBackUp is free and has active support on Twitter itself (@TweetBackUp). Once you’ve signed in (it uses your Twitter account for authentication), it automatically backs up your tweets, and you can quickly export your last 3,200 tweets into any of four formats, which you can then search. As a bonus, the HTML and CSV formats give you the permanent URL for each tweet.