Heuristic models and observational analyses of atmospheric convection often assume that convective activity, for example rain rate, approaches some given value for any given large-scale (“macrostate”) environmental conditions such as static stability and humidity. We present novel convection-resolving simulations in which the convective activity evolves in a fixed equilibrium mean state (“macrostate”). In this case convective activity is unstable, diverging quasi-exponentially away from equilibrium either to extreme or zero rain rate. Thus almost any rain rate can coexist with an equilibrium profile: the model rain rate also depends on convective history. We then present a two-variable, predator-prey model motivated by this behavior, wherein small-scale (“microstate”) variability is produced by, but also promotes convective precipitation, while macrostate properties such as CAPE promote, but are consumed by convective precipitation. In this model, convection is influenced as much by its own history (via persistent microstate variability) as by its current environment. This model reproduces the simulated instability found above and could account for several lag relationships in simulated and observed convection, including its afternoon maximum over land and the well-known “quasi-equilibrium” balance at synoptic time scales between the forcing and response of key variables. These results point to a strong role for convective memory and suggests that basic strategies for observing, modeling and parameterizing convective processes should pay closer attention to persistent variability on scales smaller than that of the grid box.