The problem of direct adaptive compensation for infinite number of time-varying actuator failures/faults is of both theoretical and practical importance in the fuzzy tracking control of uncertain nonlinear systems. However, due to the technical difficulties, so far, very limited result is available in addressing such an issue, which thus motivates us to propose a new fuzzy control methodology in this paper. The proposed scheme is established from the techniques of projection adaptation design, a new piecewise Lyapunov function analysis, and an optimized fuzzy adaptation. It is shown that all the closed-loop signals are bounded and the steady-state tracking error converges to a residual around zero, irrespective of a possibility that there are infinite number of time-varying actuator failures. Simulations are provided to illustrate the effectiveness and applicability of the proposed scheme.