Knowledge-intensive language tasks (KILTs) typically require retrieving relevant documents from trustworthy corpora, e.g., Wikipedia, to produce specific answers. Very recently, a pre-trained generative retrieval model for KILTs, named CorpusBrain, was proposed and reached new state-of-the-art retrieval performance. However, most existing research on KILTs, including CorpusBrain, has predominantly focused on a static document collection, overlooking the dynamic nature of real-world scenarios, where new documents are continuously being incorporated into the source corpus. To address this gap, it is crucial to explore the capability of retrieval models to effectively handle the dynamic retrieval scenario inherent in KILTs. In this work, we first introduce the continual document learning (CDL) task for KILTs and build a novel benchmark dataset named KILT++ based on the original KILT dataset for evaluation. Then, we conduct a comprehensive study over the use of pre-trained CorpusBrain on KILT++. Unlike the promising results in the stationary scenario, CorpusBrain is prone to catastrophic forgetting in the dynamic scenario, hence hampering the retrieval performance. To alleviate this issue, we propose CorpusBrain++, a continual generative pre-training framework. Empirical results demonstrate the significant effectiveness and remarkable efficiency of CorpusBrain++ in comparison to both traditional and generative IR methods.