Accurate segmentation of thin curvilinear structures is vital for various real-world applications, from vessel analysis to road extraction. Yet their intricate geometry makes even minor pixel-wise errors enough to break the global topology, and this structural fragility turns severe domain shifts into catastrophic failures. The difficulty is most acute under cross-modality gaps, where the imaging process itself differs fundamentally between source and target. While test-time adaptation (TTA) offers a practical source-free remedy, existing methods adapt feature statistics and confidence, neither of which constrains connectivity, and thus degrade under such extreme gaps. To address this, we propose Skeleton-Guided Progressive Test-Time Adaptation (SGP-TTA). Progressive Batch Normalization (ProgBN) shifts normalization from frozen source statistics toward current target estimates under a sample-count schedule, so that the source-target balance follows the stage of adaptation rather than a fixed coefficient. Consensus Skeleton Recall (CSR) then derives a structural target from geometrically aligned multi-view predictions and updates only the BN affine parameters to preserve connected structures. Extensive experiments show that SGP-TTA consistently outperforms existing TTA methods in topological connectivity, with the largest margins under cross-modality shift. The project page is available at https://boa-jang.github.io/SGP-TTA.

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