We state a position on addressing the problem of Zero Downtime Edge Application Mobility (ZeroDEAM) for ultra-low latency 5G streaming services. We define and use an Edge network gaming use case as a paradigm for investigating a solution to contemporary and emerging 5G use cases characterized by high mobility and ultra-low latency, and which require zero downtime after handover. As a solution thesis, we pose a conceptual architecture leveraging Machine Learning (ML) potential at the network’s Edge, where distributed intelligent models in the proximity of mobile users can take proactive or reactive actions such as regarding mobility prediction and dynamic system parameter fine-tuning to guarantee zero downtime. Our vision is to span across Multi-access Edge Computing (MEC) standardised approaches to application mobility and the wider research outside the standards domain, and in doing so bring disruptive innovation to the problem space. We back our ZeroDEAM thesis by a meticulous technical background discussion and a model analysis that set the proper latency optimisation targets, which can capture important cost trade-offs and challenges for tuning system parameters. In further, we provide a proof of concept demonstration of our Edge architecture based on a blueprint implementation, which validates our design by exhibiting zero downtime potential against "conventional" Edge app migration. Based on our discussion, analysis and early performance demonstration, we pave our way to move forward with our stated conceptual Edge architecture based on a concrete action plan addressing a set of fundamental technical and research challenges with Edge-deployed intelligent models.