Convection is often assumed to be controlled by the simultaneous environmental fields. But to what extent does it also remember its past behavior? This study proposes a new framework in which the memory of previous convective-scale behavior, "microstate memory," is distinguished from macrostate memory, and conducts numerical experiments to reveal these memory types. A suite of idealized, cloud-resolving radiative-convective equilibrium simulations in a 200-km square domain is performed with the Weather Research and Forecasting (WRF) Model. Three deep convective cases are analyzed: unorganized, organized by low-level wind shear, and self-aggregated. The systematic responses to sudden horizontal homogenization of various fields, in various atmospheric layers, designed to eliminate their specific microstructure, are compared in terms of precipitation change and time of recovery to equilibrium. Results imply a substantial role for microstate memory. Across organization types, microstructure in water vapor and temperature has a larger and longer-lasting effect on convection than in winds or hydrometeors. Microstructure in the subcloud layer or the shallow cloud layer has more impact than in the free troposphere. The recovery time scale dramatically increases from unorganized (2-3 h) to organized cases (24 h or more). Longer-time-scale adjustments also occur and appear to involve both small-scale structures and domain-mean fields. These results indicate that most convective microstate memory is stored in low-level thermodynamic structures, potentially involving cold pools and hot thermals. This memory appears strongly enhanced by convective organization. Implications of these results for parameterizing convection are discussed.