The increasing demand for wireless communication underscores the need to optimize radio frequency spectrum utilization. An effective strategy for leveraging underutilized licensed frequency bands is cooperative spectrum sensing (CSS), which enable multiple secondary users (SUs) to collaboratively detect the spectrum usage of primary users (PUs) prior to accessing the licensed spectrum. The increasing popularity of machine learning has led to a shift from traditional CSS methods to those based on deep learning. However, deep learning-based CSS methods often rely on centralized learning, posing challenges like communication overhead and data privacy risks. Recent research suggests vertical federated learning (VFL) as a potential solution, with its core concept centered on partitioning the deep neural network into distinct segments, with each segment is trained separately. However, existing VFL-based CSS works do not fully address the practical challenges arising from streaming data and the objective shift. In this work, we introduce online vertical federated learning (OVFL), a robust framework designed to address the challenges of ongoing data stream and shifting learning goals. Our theoretical analysis reveals that OVFL achieves a sublinear regret bound, thereby evidencing its efficiency. Empirical results from our experiments show that OVFL outperforms benchmarks in CSS tasks. We also explore the impact of various parameters on the learning performance.