It is known that Abhimanyu, son of Arjuna, was killed during the Chakra Vyuh (a.k.a Padmavyuha) in the war.
Why did he die? Why couldn't Lord Krishna save him? Was he destined to die in this way?
First of all, Krishna couldn't have intervened and saved him directly, because he had taken a vow not to fight. Second of all, Krishna and Arjuna were busy fighting Susharma at the time, while the rest of the Pandava army couldn't get to Abhimanyu because they were blocked by Duhsala's husband Jayadratha (which is why Arjuna took revenge on Jayadratha afterward).
But more fundamentally, the real reason why Abhimanyu was killed is because, as I discuss in this answer, he was an incarnation of Varchas, son of Chandra the moon god, and Chandra didn't want to be apart from his son for too long. Here is what this chapter of the Adi Parva of the Mahabharata says:
And he who was known as the mighty Varchas, the son of Soma, became Abhimanyu of wonderful deeds, the son of Arjuna. And before his incarnation, O king, the god Soma had said these words to the celestials, 'I cannot give (part with) my son. He is dearer to me than life itself. Let this be the compact and let it be not transgressed. The destruction of the Asuras on earth is the work of the celestials, and, therefore, it is our work as well. Let this Varchas, therefore, go thither, but let him not stay there long.'
It's similar to why the Upapandavas, the five sons of Draupadi, died at a young age, as I discuss here.