Social Media (SM) has become a valuable information source to many in diverse situations. In IR, research has focused on real-time aspects and as such little is known about how long SM content is of value to users, if and how often it is re-accessed, the strategies people employ to re-access and if difficulties are experienced while doing so. We present results from a 5 month-long naturalistic, log-based study of user interaction with Twitter, which suggest re-finding to be a regular activity and that Tweets can offer utility for longer than one might think. We shed light on re-finding strategies revealing that remembered people are used as a stepping stone to Tweets rather than searching for content directly. Bookmarking strategies reported in the literature are used infrequently as a means to re-access. Finally, we show that by using statistical modelling it is possible to predict if a Tweet has future utility and is likely to be re-found. Our findings have implications for the design of social media search systems and interfaces, in particular for Twitter, to better support users re-find previously seen content.