Due to the limited energy resources in a wireless sensor network (WSN), lifetime of a WSN is a key parameter. In this paper, we address a lifetime optimization problem of a wireless TDMA/CDMA sensor network for joint transmit power and rate allocations in a time-varying fast Rayleigh fading environment. The effect of fast fading is captured by including rate outage and link outage constraints on each link and a given time-slot. A resulting nonconvex problem is then reduced to an approximate convex optimization problem using an appropriate functional approximation and variable substitutions. This centralized problem is then solved by standard barrier-method based optimization algorithms. A partially distributed algorithm is also provided to illustrate how most of the computations can be done locally at each node in a decentralized manner. The novelty of the paper lies in considering fast fading channels via outage probability constraints for the first time in lifetime maximization problems and obtaining a better convex approximation than previously used approximations in the literature. Simulation results illustrate that our centralized algorithm results in optimal power and rate allocations that result in a substantially extended lifetime of the WSN compared to previously published algorithms. The convergence of the partially distributed algorithms to the optimal power and rate solutions is also illustrated.