In the context of the booming digital economy, recommendation systems, as a key link connecting users and numerous services, face challenges in modeling user behavior sequences on local-life service platforms, including the sparsity of long sequences and strong spatio-temporal dependence. Such challenges can be addressed by drawing an analogy to the forgetting process in human memory. This is because users' responses to recommended content follow the recency effect and the cyclicality of memory. By exploring this, this paper introduces the forgetting curve and proposes Spatio-Temporal periodic Interest Modeling (STIM) with long sequences for local-life service recommendation. STIM integrates three key components: a dynamic masking module based on the forgetting curve, which is used to extract both recent spatiotemporal features and periodic spatiotemporal features; a query-based mixture of experts (MoE) approach that can adaptively activate expert networks under different dynamic masks, enabling the collaborative modeling of time, location, and items; and a hierarchical multi-interest network unit, which captures multi-interest representations by modeling the hierarchical interactions between the shallow and deep semantics of users' recent behaviors. By introducing the STIM method, we conducted online A/B tests and achieved a 1.54\% improvement in gross transaction volume (GTV). In addition, extended offline experiments also showed improvements. STIM has been deployed in a large-scale local-life service recommendation system, serving hundreds of millions of daily active users in core application scenarios.