Could the Child of Prophecy not die?
Of course they could. Both Minato Namikaze and Nagato, whom Jiraiya had considered Children of Prophecy, had died.
Then the question was, why could Jiraiya not kill the Child of Prophecy?
Did the mere identity of a Child of Prophecy make Jiraiya regard them differently, leaving him unable to move his feet or raise his kunai?
Oguri Hayashi's A Sudden Enlightenment woke Jiraiya up. Right—the future was merely the future, and a prophecy was merely a prophecy. What did it have to do with him? He, the Toad Sage, was not the Child of Prophecy. If he killed them, that only meant they were not the Child of Prophecy!
Third Hokage Hiruzen Sarutobi had laid out four matters in total.
First, ensure the appearance of Sage Naruto. In other words, the Fourth Hokage position had already been reserved for Minato Namikaze. Second, hunt down Madara.
Although Uchiha Madara was powerful, he was not invincible. Never mind that he was already seventy or eighty years old and nearing the end of his life—even in his prime, the Ninja Hero together with the current Three Sannin would not have lacked the strength to fight him.
Now was the time to strike while he was weak and take his life. Killing Uchiha Madara sooner would disrupt who knew how many of his arrangements. Besides, NARUTO was a full 700-chapter epic spanning the era from the Third Hokage to the Seventh Hokage. If Uchiha Madara died now, his chances of resurrection in the future would diminish by a little, and Kaguya Ōtsutsuki's chances of resurrection would diminish by even more.
The best outcome would be preventing Kaguya Ōtsutsuki's resurrection entirely. If that truly could not be stopped, then they had to ensure Sage Naruto's growth.
Thus, on