Memory processes in complex behaviors like social communication require forming representations of the past that grow with time. The neural mechanisms that support such continually growing memory remain unknown. We address this gap in the context of fly courtship, a natural social behavior involving the production and perception of long, complex song sequences. To study female memory for male song history in unrestrained courtship, we present 'Natural Continuation' (NC)-a general, simulation-based model comparison procedure to evaluate candidate neural codes for complex stimuli using naturalistic behavioral data. Applying NC to fly courtship revealed strong evidence for an adaptive population mechanism for how female auditory neural dynamics could convert long song histories into a rich mnemonic format. Song temporal patterning is continually transformed by heterogeneous nonlinear adaptation dynamics, then integrated into persistent activity, enabling common neural mechanisms to retain continuously unfolding information over long periods and yielding state-of-the-art predictions of female courtship behavior. At a population level this coding model produces multi-dimensional advection-diffusion-like responses that separate songs over a continuum of timescales and can be linearly transformed into flexible output signals, illustrating its potential to create a generic, scalable mnemonic format for extended input signals poised to drive complex behavioral responses. This work thus shows how naturalistic behavior can directly inform neural population coding models, revealing here a novel process for memory formation.