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The emergence of latency-critical AI applications has been supported by the evolution of the edge computing paradigm. However, edge solutions are typically resource-constrained, posing reliability challenges due to heightened contention for compute and communication capacities and faulty application behavior in the presence of overload conditions. Although a large amount of generated log data can be mined for fault prediction, labeling this data for training is a manual process and thus a limiting factor for automation. Due to this, many companies resort to unsupervised fault-tolerance models. Yet, failure models of this kind can incur a loss of accuracy when they need to adapt to non-stationary workloads and diverse host characteristics. To cope with this, we propose a novel modeling approach, called DeepFT, to proactively avoid system overloads and their adverse effects by optimizing the task scheduling and migration decisions. DeepFT uses a deep surrogate model to accurately predict and diagnose faults in the system and co-simulation based self-supervised learning to dynamically adapt the model in volatile settings. It offers a highly scalable solution as the model size scales by only 3 and 1 percent per unit increase in the number of active tasks and hosts. Extensive experimentation on a Raspberry-Pi based edge cluster with DeFog benchmarks shows that DeepFT can outperform state-of-the-art baseline methods in fault-detection and QoS metrics. Specifically, DeepFT gives the highest F1 scores for fault-detection, reducing service deadline violations by up to 37\% while also improving response time by up to 9%.