With the development of sixth-generation (6G) mobile networks, the rise of emerging intelligent services has led to a huge increase in traffic. As an important technology to support the development of 6G, mobile edge computing (MEC) effectively meets the ultra-low latency requirements of most emerging services. However, due to the limited processing capacity of edge nodes, overload on any edge node will cause service degradation, interruption, and even node failure, weakening the advantages of MEC and reducing the survivability of the whole network. In this paper, we propose a task offloading scheme based on traffic prediction for node-overload protection to ensure the survivability of the 6G edge networks. We transformed the network survivability guarantee problem into a task offloading problem under the constraint of future available resources based on traffic prediction and developed a particle swarm optimization algorithm based on policy gradient (PSO-PG) to jointly optimize offloading decisions, routing, and computing resource allocation. Simulations verify the effectiveness of our proposed scheme and guarantee the survivability of 6G edge networks. Meanwhile, evaluation in multiple scenarios with different node scales has verified the wide applicability of our work.