A key challenge for random access communications arising in the monitoring of physical phenomena is optimizing the access policy. This is particularly the case when the activity of each sensor is correlated, contrasting with the independence assumption underpinning standard slotted ALOHA schemes. In this paper, we propose a stochastic resource allocation algorithm to reduce outages via maximization of the expected number of sensors that are able to reliably communicate with an access point. Allowing for devices to transmit data over multiple consecutive frames, we show that the proposed algorithm converges with probability one to a locally optimal solution. Moreover, our algorithm significantly outperforms existing methods in terms of the average number of successful transmissions when utilizing successive interference cancellation.