ことなく means 'without doing (even once)'. It emphasizes that the action in the clause was completely avoided throughout the entire situation. It is often used in narratives, reports, or formal contexts to highlight a remarkable achievement or a surprising absence of something. For example, you might say someone worked for decades without taking a single day off, or a team won the championship without losing a game all season. The pattern is more formal than ないで or ずに, so it is common in written Japanese (news, essays, speeches) rather than everyday conversation. In casual speech, you would typically use ないで or なくて.