Interest in coated microbubbles as agents for therapeutic and quantitative imaging applications in biomedical ultrasound has increased the need for their accurate theoretical characterization. Effects such as gas diffusion, variation in the properties of the coating and the resulting changes in bubble behavior under repeated exposure to ultrasound pulses are, however, still not well understood. In this study, a revised equation for microbubble motion is proposed that includes the effects of gas diffusion, as well as adsorption, desorption and shedding of a surfactant from the bubble surface. This is incorporated into a nonlinear wave propagation model to account for these additional time dependent effects in the response of microbubble populations. The results from the model indicate there can be significant changes in both bubble behavior and the propagated pulse over time. This is in agreement with existing experimental data but is not predicted by existing propagation models. The analysis indicates that changes in bubble dynamics are dominated by surfactant shedding on the timescale of a diagnostic ultrasound pulse and gas diffusion over the timescale of the pulse repetition frequency. The implications of these results for the development of more accurate algorithms for quantitative imaging and for therapeutic applications are discussed.