In this paper, we analyze the packet transmission time in a cognitive cooperative radio network (CCRN) where a secondary transmitter (SU-Tx) sends packets to a secondary receiver (SU-Rx) through the help of a secondary relay (SR). In particular, we assume that the SU-Tx and SR are subject to the joint constraint of the timeout probability of the primary user (PU) and the peak transmit powers of the secondary users. On this basis, we investigate the impact of the transmit power of the PUs and channel mean powers on the packet transmission time of the CCRN. Utilizing the concept of timeout, adaptive transmit power allocation policies for the SU-Tx and SR are considered. More importantly, analytical expressions for the endto- end throughput, end-to-end packet transmission time, and stable condition for the SR operation are obtained. Our results indicate that the second hop of the considered CCRN is not a bottleneck if the channel mean powers of the interference links of the networks are small and the SR peak transmit power is set to a high value.