The Lindy effect is a statistical tendency for things with longer pasts behind them to have longer futures ahead. It has been experimentally confirmed to apply to some categories, but not others, raising questions about when it is applicable and why. I shed some light on these questions by examining the mathematical properties required for the effect and generating mechanisms that can produce them. While the Lindy effect is often thought to require a declining hazard rate, I show that it arises very naturally even in cases with constant (or increasing) hazard rates -- so long as there is a probability distribution over the size of that rate. One implication is that even things which are becoming less robust over time can display the Lindy effect.