In this work, we give a complete characterization of the epsilon-stable region in dynamic downlink random cellular networks. The epsilon-stable region is the set of arrival rates such that the proportion of unstable queues in the network is not larger than epsilon. We derive upper and lower bounds as well as an approximation of the critical arrival rate, which delimits the epsilon-stable region. The developed model is based on stochastic geometry and queuing theory to handle the interaction between the transmit success probability and the queuing state evolution. Extensive numerical simulations are provided to confirm the tightness of the approximation.