Currently, sentiment analysis research is generally based on big data-driven models, which heavily rely on expensive annotation and computational costs. Therefore, research on sentiment analysis in low-resource scenarios is particularly urgent. However, existing research on sentiment analysis in low-resource scenarios mainly focuses on a single task, making it difficult for models to acquire external task knowledge. Therefore, this study constructs successive sentiment analysis in low-resource scenarios, aiming to allow models to learn multiple sentiment analysis tasks over time by continual learning methods. This can make full use of data from different tasks and learn sentiment information from different tasks, thus alleviating the problem of insufficient training data for a single task. There are two core problems with successive sentiment analysis in low-resource scenarios. One is preserving sentiment information for a single task, and the other is fusing sentiment information between different tasks. To solve these two problems, this study proposes continual attention modeling for successive sentiment analysis in low-resource scenarios. Sentiment masked Adapter (SMA) is first constructed, which is used to generate hard attention emotion masks for different tasks. This can preserve sentiment information for different tasks and mitigate catastrophic forgetting. Secondly, dynamic sentiment attention (DSA) is proposed, which dynamically fuses features extracted by different Adapters based on the current time step and task similarity. This can fuse sentiment information between different tasks. Experimental results on multiple datasets show that the proposed approach significantly outperforms the state-of-the-art benchmark approaches. Additionally, experimental analysis indicates that the proposed approach has the best sentiment information retention ability and sentiment information fusion ability compared to other benchmark approaches while maintaining high operational efficiency.