Performance evaluation of the IEEE 802.11e network has been the subject of several research papers. Especially, the transmission opportunity limit (TXOPLimit) has been proven efficient for achieving differentiated quality of service (QoS) and improving the wireless bandwidth utilisation. However, most existing analytical models have been developed under unrealistic assumption that the wireless channel is error-free. Hence, the efficiency and the performance level of the TXOPLimit in an error-prone channel are questionable. In this paper, we aim at proposing a new Markov chain model of the IEEE 802.11e network including the TXOPLimit and the packet error rate (PER). Then, we derive the saturation throughput of the IEEE 802.11e network in cases of aggregated and non-aggregated packets. The obtained results show that, the TXOPLimit efficiency is highly degraded under the effect of bit error rate (BER) and packet length.