This paper is the first extensive work on FIFO order reliable convergecast in multi-hop Wireless Body Area Networks (WBAN). Convergecast is a many-to-one cooperative scheme where each node of the network transmits data towards the same sink. In critical application of WBAN such as medical, packets loss or inversion have an important impact at the application level. Our contribution is threefold. First, we stress existing WBAN convergecast strategies with respect to their capacity to be reliable and verify the FIFO order of message reception (packets sent in a specific order by a node should be received in the same order by the sink). When stressed with transmission rates up to 500 packets per second and various human body postures, the performances of all these strategies decrease dramatically (more than 90% of packets are lost). This dramatic reliability drop has never been exposed in wireless body area network. Secondly, we propose a new posture-centric link model for WBAN. This model offers a good characterization of paths availability from each node to the sink, and is further used to fine tune the retransmission rates. Third, based on our model we propose a new mechanism for reliability, Non-ACK Retransmission, and a new converge-cast tree based strategy that outperforms WBAN dedicated strategies but also strategies adapted from DTN and WSN areas. We performed extensive evaluations with seven different human body postures. We targeted the following parameters: packet loss, FIFO order reliability and energy consumption. Our new strategy ensures zero packet order inversions for various transmission rates and mobility postures. Interestingly, our strategy verifies this property without the need of additional energy-guzzler mechanisms.