Deflagration waves propagating through porous energetic materials are known to be subject to intrinsic diffusional/thermal instabilities that are associated with the onset of various oscillatory modes of combustion. A few theoretical analyses to explain these combustion phenomena have been published in the literature, and the present contribution extends these results. In particular, we reconsider our previous asymptotic analysis of non-steady, non-planar deflagration, which postulated a constant-density gas phase, to take into account the effects of quasi-steady thermal expansion of an ideal gas. With relative motion between gaseous and condensed phases included, a time-dependent, multidimensional asymptotic model is derived through the application of activation-energy asymptotics. Analyzing this model, an explicit solution corresponding to steady, planar deflagration is obtained as a special case, and a dispersion relation is derived describing its linear stability. In the plane defined by the non-dimensional activation energy and the disturbance wavenumber, a pulsating neutral stability boundary is calculated, beyond which non-steady, non-planar solutions are expected. The effects of porosity and gas-phase thermal expansion are shown to be generally destabilizing, suggesting that degraded propellants, which exhibit greater porosity than the pristine material, may be more readily subject to combustion instability and non-steady deflagration.