State space models (SSMs) achieve efficient sub-quadratic compute complexity but often exhibit significant performance drops as context length increases. Recent work attributes this deterioration to an exponential decay in hidden-state memory. While token filtering has emerged as a promising remedy, its underlying rationale and limitations remain largely non-understood. In this paper, we first investigate the attention patterns of Mamba to shed light on why token filtering alleviates long-context degradation. Motivated by these findings, we propose LAMB, a training-free, attention-guided token filtering strategy designed to preserve critical tokens during inference. LAMB can boost long-context performance for both pure SSMs and hybrid models, achieving up to an average improvement of 30.35% over state-of-the-art techniques on standard long-context understanding benchmarks. Our analysis and experiments reveal new insights into the interplay between attention, token selection, and memory retention, and are thus expected to inspire broader applications of token filtering in long-sequence modeling.