In this paper, a novel adaptive failure compensation scheme is designed for near space vehicles (NSVs) which belong to a class of affine nonlinear MIMO systems, prone to actuator float free, stuck and oscillatory failures, unknown in time, pattern and magnitude. The proposed control methodology utilizes a backstepping procedure based on an adaptive finite time disturbance observer to estimate failure induced uncertainties and external disturbances. The proposed failure compensation scheme ensures effective failure accommodation in finite time while providing excellent transient and steady state performances even when three input failures occur simultaneously. Stability and asymptotic tracking in presence of unknown actuator failures at unknown time instants using the proposed control scheme as well as finite time stability of the adaptive finite time disturbance observer is proved using Lyapunov criterion. Simulation results illustrate the effectiveness of the proposed methodology in application to NSVs.