We study the evolution of the number of retweets received by Twitter users over the course of their 'careers' on the platform. We find that on average the number of retweets received by users tends to increase over time. This is partly expected because users tend to gradually accumulate followers. Normalizing by the number of followers, however, reveals that the relative, per-follower retweet rate tends to be non-monotonic, maximized at a 'peak age' after which it does not increase, or even decreases. We develop a simple model of the process behind this phenomenon, which assumes a constantly growing number of followers, each of whom loses interest over time. We show that this model is sufficient to explain the non-monotonic nature of per-follower retweet rates, without any assumptions about the quality of content posted at different times.