This paper focuses on the treatment of uplink traffic of the highest data priority, i.e. Emergency traffic in the 802.15.6 standard for a wireless body area network (WBAN). This standard is one of the choices available for the so-called wearable Internet or wireless connection between electronic devices worn on or implanted in the human body. The features for positive discrimination of emergency traffic are identified at three different components in the 802.15.6 standard in order to emphasize the importance of its prioritized delivery that must be always preserved due to potential applications in the field of monitoring of health variables. However, prioritization could be compromised by the anomaly in the medium access under contention algorithms in standard 802.15.6. That is the reason that we find it appropriate to address the anomaly, i.e. to describe a sequence of packets that can bring a station into the state in which it sends highest-priority data frames with the parameters of the back-off algorithm used for traffic with a significantly lower priority and thus reduces the station's chances to access the medium. The main contribution of this work is to identify the set of five conditions that must be met at the same time in order to make the anomaly to appear, and explain that the scene for anomaly manifestation would be set up periodically in secured communication. We provide a simulation study and discussion on the available solutions for preventing this anomaly including a minor change to the algorithm at the level of the standard.