Exponential decay laws describe systems ranging from unstable nuclei to fluorescent molecules, in which the probability of jumping to a lower-energy state in any given time interval is static and history-independent. These decays, involving only a metastable state and fluctuations of the quantum vacuum, are the most fundamental nonequilibrium process and provide a microscopic model for the origins of irreversibility. Despite the fact that the apparently universal exponential decay law has been precisely tested in a variety of physical systems, it is a surprising truth that quantum mechanics requires that spontaneous decay processes have nonexponential time dependence at both very short and very long times. Cold-atom experiments have proven to be powerful probes of fundamental decay processes; in this article, we propose the use of Bose condensates in Floquet-Bloch bands as a probe of long-time nonexponential decay in single isolated emitters. We identify a range of parameters that should enable observation of long-time deviations and experimentally demonstrate a key element of the scheme: tunable decay between quasi-energy bands in a driven optical lattice.