Existing Visual Simultaneous Localization And Mapping (vSLAM) approaches that offload the complex self-localization computations from mobile robots over a wireless network to edge computing are limited to static offloading, i.e., the offloaded computation tasks are offloaded permanently. However, wireless networks are inherently dynamic and may excessively delay the transmissions between a mobile device and the edge during periods of poor wireless network quality, e.g., from fading or temporary obstructions. We propose and evaluate Dynamic Visual SLAM Network Offloading (DynNetSLAM) to dynamically adapt the vSLAM computation offloading according to the measured wireless network latency. As groundwork towards developing DynNetSLAM, we first enhance the existing state-of-the-art vSLAM approaches through judicious parameter settings and parallel map updates to enable the tracking of common fast vSLAM data sets. We introduce an offloading latency threshold along with a safe zone and a hysteresis around the threshold to control the dynamic offloading. Our extensive evaluations with public vSLAM data sets indicate that DynNetSLAM with the hysteresis substantially reduces the probability of track loss events compared to the state-of-the-art ORB-SLAM2 approach for processing statically on the mobile device and the enhanced static Edge SLAM. Also, DynNetSLAM nearly attains the low absolute position error and only slightly increases the CPU utilization compared to the enhanced static Edge SLAM.