A reactive-power-based model reference adaptive system updating rotor time constant in induction motor drives has been researched for many years; however, it is still required to improve it further in some aspects for more wide applicability in practice. First, the information of stator frequency is incorporated into the adaptive mechanism, by which not only the effective range of the updating scheme is extended, but also the open-loop gain, otherwise relating with the quantity of stator frequency closely, is normalized facilitating the design of the adaptation gains. Second, two equilibrium points (EPs) of the reactive power model are found out and identified as the desired EP and zero-frequency EP, paving a way to stability analysis and refined design criterions. Third, since the high-nonlinearity characteristic of the system prevents the Routh-Hurwitz criterion from being used to the stability analysis, a small-signal model of the estimation system is established. It is revealed that the adaptive scheme, obtained through the Lyapunov theorem by neglecting rotor flux dynamics, is not always stable as commonly accepted. In this paper, the stability properties of the two EPs and the mechanism behind the instability phenomena are explored with the help of the developed small-signal model, which supplies theoretical basis to predict the stability of the reactive power model. Furthermore, the design strategy of adaptation proportional-integral gains is proposed, allowing the stability as well as the dynamic performance to be improved throughout the operation range. The proposed analysis has been validated through experiments.