In this work, we address the problem of finding optimal transmit power control policies for wireless energy harvesting sensors (EHS) with automatic repeat request (ARQ)-based packet (re)transmissions. The policy is designed to minimize the average probability of packet outage, under the constraint of long-term energy neutrality at the EH node. The indirect information about the channel state gleaned through ACK/NACK messages is used to set the transmit power of each packet attempt. Using tools from convex optimization, we obtain an optimal power management policy, under the assumption of an ideal, infinite-capacity battery. By design, the policy operates independent of the current battery state, and is therefore suitable in scenarios where it is difficult or energy-expensive to obtain accurate battery state information. Also, the optimal solution is computationally very simple to evaluate. We validate our results using Monte Carlo simulations, and show that the proposed policy outperforms existing state-of-the-art transmission schemes.