Long-range, low-power wireless technologies such as LoRa have been shown to exhibit excellent performance when applied in body-centric wireless applications. However, the robustness of LoRa technology to Doppler spread has recently been called into question by a number of researchers. This paper evaluates the impact of static and dynamic Doppler shifts on a simulated LoRa symbol detector and two types of simulated LoRa receivers. The results are interpreted specifically for body-centric applications and confirm that, in most application environments, pure Doppler effects are unlikely to severely disrupt wireless communication, confirming previous research, which stated that the link deteriorations observed in a number of practical LoRa measurement campaigns would mainly be caused by multipath fading effects. Yet, dynamic Doppler shifts, which occur as a result of the relative acceleration between communicating nodes, are also shown to contribute to link degradation. This is especially so for higher LoRa spreading factors and larger packet sizes.