Wireless Body Area Networks (WBANs) have received much attention due to the possibility to be used in healthcare applications. For these applications, energy saving is a critical issue, as in many cases, batteries cannot be easily replaced. A transmit power control scheme, able to adapt to the variations of the wireless body channel, will allow consistent energy saving and longer battery life. In this paper we propose a transmit power control scheme suitable for IEEE 802.15.6 narrowband scheduled access networks, in which the transmission power is modulated frame by frame according to a run-time estimation of the channel propagation conditions. A simple and effective line search algorithm is proposed to estimate the channel quality based on the signal power received from the hub; in addition, an adaptive fade margin estimator is presented to determine an optimum margin based on the channel conditions. The approach allows tracking the highly variable propagation conditions due to the body mobility and the deployment of the sensors close to the human body. An experimental study in different test cases proves the effectiveness of the scheme in comparison with alternative solutions in the literature.