This paper describes a new platform enabling continuous testing and SLA management of private wireless networks (i.e., LTE and 5G) for industrial automation. The basic principle of the platform is that industrial wireless networks need to be tested continuously as the environment might change continuously. Given the complexity and variety of current factory use cases, we argue that network capabilities must be characterized continuously, on a per-UE (User Equipment), and per SLA fashion. In this perspective, the platform described in this paper enables i) the creation and management of SLA definitions through a custom-built SLA compiler, ii) all the automation needed to continuously test the network continuously, according to the defined SLAs. The platform includes a dedicated embedded hardware and a cloud-native back end providing services at the network core level. Results from field deployment in several production 5G networks for factory automation show that the platform can substantially reduce the testing cost and enable new use cases, like Autonomous Guided Vehicles-driven automated network testing.