Test-time adaptation (TTA) promises robustness under distribution shift by updating a pretrained model on unlabeled test data, but strict online TTA with batch size one and no access to source data is especially prone to drift or collapse. We introduce Sensitivity-Guided Erasing Adaptation (SEGA), a method for strict online continual TTA (CTTA) on corruption-style streams. SEGA uses a small number of structured erasures to probe how predictive entropy changes as information is removed, and uses the resulting per-sample sensitivity trajectories to coordinate recovery and sample selection rather than relying on raw entropy or batch statistics. This yields a practical feedback signal for long-horizon batch-size-one adaptation without periodic resets or model reservoirs. In experiments on ImageNet-C, CIFAR10/100-C, and corruption-generated aquaculture streams treated as controlled corruption-style proxies, SEGA yields consistent robustness and stability gains over strong CTTA baselines while reducing backward passes through sensitivity-based gating.