To hold out, stand firm, or endure (against pressure, hardship, or attack).
彼らは厳しい寒さに踏みこたえて作業を続けた。
They endured the severe cold and continued their work.
攻撃を受けたが、防衛線は踏みこたえた。
They came under attack, but the defensive line held.
この建物は古いが地震に踏みこたえた。
This building is old, but it withstood the earthquake.