We study error propagation in wireless cooperative broadcast protocols. In our model, nodes in the network are randomly deployed in a fixed region. The message from a certain source node is relayed by multiple groups of cooperating relays that are located in predetermined consecutive swaths of the network area. We refer to these groups of relays as "levels". Our analysis is based on the derivation of recursive equations that express the error rate at each relay in a given level as a function of the error probabilities of the nodes in the previous levels. To provide analytical results we take the limit as the number of nodes goes to infinity while the relay power goes to zero, so that the relay power density pelunit area, is constant. In the limit, we show that the relay power density and area of the regions that correspond to the levels lead to fixed points in the error rate that prevent catastrophic error propagation, regardless of the distance the message is transmitted over.