Wireless body area network (WBAN) has become a promising technology, which can be widely applied in health monitoring, and so on. However, the performance of a practical WBAN may severely suffer from the degradation caused by dynamic nature of wireless channels with the movements of human body. Traditional communication frameworks cannot catch up with the channel variation of dynamic WBANs, which may severely degrade the performance, so an accurate channel prediction model is necessary for developing an efficient transmission strategy. In this paper, we propose a DeepBAN communication framework for dynamic WBANs. In our proposed framework, a temporal convolution network (TCN) based deep learning approach is adopted for channel prediction, the computationally intensive task of which is processed by mobile edge computing (MEC), to reduce the response time. Given the predicted channel conditions, we propose a joint power control, time-slot allocation, and relay selection algorithm to maximize the energy efficiency of the system, taking into account the transmission reliability and end-to-end latency requirements. We evaluate the performance of DeepBAN, and the results show that it can achieve energy-efficient, reliable, and low-latency data transmission in dynamic WBANs, which can improve the system energy efficiency by 15% compared with the stochastic scheduling scheme.