Twitter content visibility ages quickly — yesterday's news is todays chip shop wrapping paper. However, not all Twitter content of value ages badly. Yes, Google, Bing, and the like use Twitter for social signals but current content is mostly favored over older tweets. Outside of time-bound announcements there is wealth of content from brands that tips over the Twitter waterfall into oblivion — top tips, cool videos, white papers, quotes, free music tracks, and other media goodness that has a much longer shelf life than the perpetually scrolling Twitter feed can keep up with.
There are many services that offer an attractive magazine-style landing page that aggregates all activity on your tweet stream, such as paper.li, but the problem from the brand perspective is that it is all content on your tweet stream — not just your own posts. That approach is fine for broad curation of ideas and topics but not for promoting a brand or individual. Other services like news.me provide magazine-style presentation of your Twitter content, but the problem from the marketer's point of view is that the content is locked up inside a smartphone app that doesn't garner search engine attention — it's a private reader not a public profile.