to stay on; to remain; to hold out; to hold one's ground
to stop (doing); to give up
兵士は激戦で踏み止まった。
The soldier held his ground in the fierce battle.
彼は会社に踏み止まって昇進した。
He stayed on at the company and got promoted.
暴落時でも株を売らずに踏み止まるべきだ。
Even during a market crash, you should hold out and not sell your stocks.