This paper deals with the stability analysis of the well-known Adaptive Full-Order Observer for the speed estimation of induction motor drive in a motoring and regenerating mode, under motor parameter mismatch. The influence of the identification errors of the stator and rotor resistance and magnetizing inductance on unstable operating points regions of the estimator with the modified adaptation algorithm for the regenerating mode are discussed. The changes of stability regions and torque-speed characteristics of the drive under parameter uncertainties are shown and discussed in the paper for the observer with the speed adaptation law modified by the shift angle between the stator current error and rotor flux vectors. Simulation and experimental results confirming the theoretical analysis are presented.