Over days and weeks, neurons in mammalian sensorimotor cortex have been found to continually change their activity patterns during performance of a learned sensorimotor task, with no detectable change in behaviour. This challenges classical theories of neural circuit function and memory, which posit that stable engrams underlie stable learned behavior [1,2]. Using existing experimental data we show that a simple linear readout can accurately recover behavioural variables, and that fixed linear weights can approximately decode behaviour over many days, despite significant changes in neural tuning. This implies that an appreciable fraction of ongoing activity reconfiguration occurs in an approximately linear subspace of population activity. We quantify the amount of additional plasticity that would be required to compensate for reconfiguration, and show that a biologically plausible local learning rule can achieve good decoding accuracy with physiologically achievable rates of synaptic plasticity.