Video paragraph captioning (VPC) involves generating detailed narratives for long videos, utilizing supportive modalities such as speech and event boundaries. However, the existing models are constrained by the assumption of constant availability of a single auxiliary modality, which is impractical given the diversity and unpredictable nature of real-world scenarios. To this end, we propose a Missing-Resistant framework MR-VPC that effectively harnesses all available auxiliary inputs and maintains resilience even in the absence of certain modalities. Under this framework, we propose the Multimodal VPC (MVPC) architecture integrating video, speech, and event boundary inputs in a unified manner to process various auxiliary inputs. Moreover, to fortify the model against incomplete data, we introduce DropAM, a data augmentation strategy that randomly omits auxiliary inputs, paired with DistillAM, a regularization target that distills knowledge from teacher models trained on modality-complete data, enabling efficient learning in modality-deficient environments. Through exhaustive experimentation on YouCook2 and ActivityNet Captions, MR-VPC has proven to deliver superior performance on modality-complete and modality-missing test data. This work highlights the significance of developing resilient VPC models and paves the way for more adaptive, robust multimodal video understanding.