Wireless Body Area Network (WBAN) technologies are emerging with extensive applications in several domains. Health is a fascinating domain of WBAN for smart monitoring of a patient's condition. An important factor to consider in WBAN is a node's lifetime. Improving the lifetime of nodes is critical to address many issues, such as utility and reliability. Existing routing protocols have addressed the energy conservation problem but considered only a few parameters, thus affecting their performance. Moreover, most of the existing schemes did not consider traffic prioritization which is critical in WBANs. In this paper, an adaptive multi-cost routing protocol is proposed with a multi-objective cost function considering minimum distance from sink, temperature of sensor nodes, priority of sensed data, and maximum residual energy on sensor nodes. The performance of the proposed protocol is compared with the existing schemes for the parameters: network lifetime, stability period, throughput, energy consumption, and path loss. It is evident from the obtained results that the proposed protocol improves network lifetime and stability period by 30% and 15%, respectively, as well as outperforms the existing protocols in terms of throughput, energy consumption, and path loss.