Can I go for an infinite high score at Donkey Kong?

Is it possible to keep jumping barrels indefinitely on level 1 of Donkey Kong to rack up a high score?

Top players say that the limit of points they could theoretically get is around 1.2 million, but it is not clear to me why that is a limit if you can just play a level indefinitely.

Solution 1:

No, I'm afraid you can't, and the reason is rather boring: each level has a time limit. If you let time expire without completing the level, you lose a life. (While the timer is labeled "Bonus", it actually will kill you.)

Achieving a high score is therefore a function of earning as many points as possible per level, while respecting the timer and not accidentally failing.