Attention-based multiple instance learning (MIL) has emerged as a powerful framework for whole slide image (WSI) diagnosis, leveraging attention to aggregate instance-level features into bag-level predictions. Despite this success, we find that such methods exhibit a new failure mode: unstable attention dynamics. Across four representative attention-based MIL methods and two public WSI datasets, we observe that attention distributions oscillate across epochs rather than converging to a consistent pattern, degrading performance. This instability adds to two previously reported challenges: overfitting and over-concentrated attention distribution. To simultaneously overcome these three limitations, we introduce attention-stabilized multiple instance learning (ASMIL), a novel unified framework. ASMIL uses an anchor model to stabilize attention, replaces softmax with a normalized sigmoid function in the anchor to prevent over-concentration, and applies token random dropping to mitigate overfitting. Extensive experiments demonstrate that ASMIL achieves up to a 6.49\% F1 score improvement over state-of-the-art methods. Moreover, integrating the anchor model and normalized sigmoid into existing attention-based MIL methods consistently boosts their performance, with F1 score gains up to 10.73\%. All code and data are publicly available at https://github.com/Linfeng-Ye/ASMIL.