Sustainable power management techniques in energy harvesting wireless sensors currently adapt the consumption of sensors to their harvesting rate within the limits of their battery residual energy, but regardless of the traffic profile. To provide a fairer distribution of the energy according to application needs, we propose a new sustainable traffic aware duty-cycle adaptation scheme (STADA) that takes into account the traffic load in addition to previous factors. We evaluate our protocol in the specific context of multi-hop IEEE 802.15.4 beacon-enabled wireless sensor networks powered by solar energy. Simulations show that our solution outperforms traffic-unaware adaptation schemes while minimizing the variance of the quality of service provided to applications.