We present a deep learning based approach to containerized application runtime stability analysis, and an intelligent publishing algorithm that can dynamically adjust the depth of process-level forensics published to a backend incident analysis repository. The approach applies variational autoencoders (VAEs) to learn the stable runtime patterns of container images, and then instantiates these container-specific VAEs to implement stability detection and adaptive forensics publishing. In performance comparisons using a 50-instance container workload, a VAE-optimized service versus a conventional eBPF-based forensic publisher demonstrates 2 orders of magnitude (OM) CPU performance improvement, a 3 OM reduction in network transport volume, and a 4 OM reduction in Elasticsearch storage costs. We evaluate the VAE-based stability detection technique against two attacks, CPUMiner and HTTP-flood attack, finding that it is effective in isolating both anomalies. We believe this technique provides a novel approach to integrating fine-grained process monitoring and digital-forensic services into large container ecosystems that today simply cannot be monitored by conventional techniques