Connected and software-defined vehicles promise to offer a broad range of services and advanced functions to customers, aiming to increase passenger comfort and support autonomous driving capabilities. Due to the high reliability and availability requirements of connected vehicles, it is crucial to resolve any occurring failures quickly. To achieve this however, a complex cloud/edge architecture with a mesh of dependencies must be navigated to diagnose the responsible root cause. As such, manual analyses become unfeasible since they would significantly delay the troubleshooting. To address this challenge, this paper presents SDVDiag, an extensible platform for the automated diagnosis of connected vehicle functions. The platform enables the creation of pipelines that cover all steps from initial data collection to the tracing of potential root causes. In addition, SDVDiag supports self-adaptive behavior by the ability to exchange modules at runtime. Dependencies between functions are detected and continuously updated, resulting in a dynamic graph view of the system. In addition, vital system metrics are monitored for anomalies. Whenever an incident is investigated, a snapshot of the graph is taken and augmented by relevant anomalies. Finally, the analysis is performed by traversing the graph and creating a ranking of the most likely causes. To evaluate the platform, it is deployed inside an 5G test fleet environment for connected vehicle functions. The results show that injected faults can be detected reliably. As such, the platform offers the potential to gain new insights and reduce downtime by identifying problems and their causes at an early stage.