It has recently been reported that, in alloys exhibiting early dynamic recrystallization (DRX), the onset of adiabatic shear bands (ASB) is primarily related to microstructural transformations, instead of the commonly assumed thermal softening mechanism as shown by Rittel et al. (2006, 2008) and Osovski et al. (2012b). Further, the dominant role of microstructural softening in the necking process of dynamically stretching rods showing DRX has been verified using linear stability analysis and finite element simulations by Rodríguez-Martínez et al. (2014). With the aim of extending this coupled methodology to shear conditions, this paper presents an analytical solution to the related problem of ASB in a material that undergoes both twinning and dynamic recrystallization. A special prescription of the initial and loading conditions precludes wave propagation in the specimen which retains nevertheless its inertia, allowing for a clear separation of material versus structural effects on the localization process. A parametric study, performed on the constants of the constitutive model, permits the identification of their relative role in the onset of the dynamic instability. The main outcome of the analysis confirms the strong destabilizing effect played by the development of DRX, consistently with the former statement regarding ASB, and contributes to rationalize the observations of other authors.