on the line

The Power of Habitから最後の引用です。
"We would practice, and everything would come together and then we'd get to a big game and it was like the training disappeared," Dungy told me. "Afterward, my players would say, 'Well, it was a critical play and I went back to what I knew,' or 'I felt like I had to step it up.' What they were really saying was they trusted our system most of the time, but when everything was on the line, that belief broke down.
"on the line" の個所が分かりそうで分かりません。辞書で意味を調べます。
・Oxford English Dictionary: At serious risk: their careers were on the line
・Cambridge Dictionary of American Idioms: at risk of failing or being harmed There's a lot of pride on the line when your book is published.
・Wiktionary: (idiomatic) At risk, as in a contest or enterprise. The survival of the company is on the line with this project.
綱渡りをしている状況を連想して覚えよう。