Bacteria and their viral predators face a constant pressure for augmented immune and infective capabilities respectively. Under this reciprocally imposed selective regime we expect to see a runaway arms race dynamic leading to rapid extinction of one species or the other. Despite this prediction, in many systems host and phage coexist with minimal coevolution. Previous work explained this puzzling phenomenon by invoking spatial structure or fitness tradeoffs, which can drive coexistence and the diminishment of an arms race dynamic. Unfortunately, these explanatory mechanisms do not apply to all systems. Here we propose a new hypothesis, that the regular loss of immunity by the bacterial host can also produce robust host-phage coexistence. We pair a general model of immunity with an experimental and theoretical case study of the CRISPR immune system to characterize and contrast the behavior of tradeoff and loss mechanisms in well-mixed systems. We find that, while both a cost of immunity and the loss of immunity can lead to stable coexistence, only a loss mechanism can do so robustly within a realistic region of parameter space.