What did Guru Dronacharya like about Arjuna?

How did Arjuna die in Mahabharata?

Arjuna eventually died once and for all after Krishna left earth while the Pandavas were trying to climb the Swargarohini Mountains to get to Swarga in their own body. Yudishthira aside, each of the remaining Pandavas fell from the Swargarohini Mountains due to a personal failure that made them unworthy of going to Swarga in their own bodies. In particular, Arjuna fell away because he was too arrogant about his fighting ability, as described in this chapter of the Swargarohanika Parva of the Mahabharata:

When he saw Nakula and the others fall, Pandu's son Arjuna of white horses, the hunter of enemy heroes, fell down with great sorrow of heart. When this foremost man, endowed with the energy of Shakra, actually fell, when this invincible hero was on the verge of death, Bhima said to the king, “I do not remember any untruth pronounced from this high. souled one. In fact, he didn't say anything wrong even in jest. Then what is it for the evil consequence of which this fell to earth? 'Yudhishthira said,' Arjuna had said that he would consume all of our enemies in a single day. He was proud of his heroism, but did not achieve what he said. That's why he fell. This phalguna ignored all bow wearers. Those who want wealth should never indulge in such feelings. '

In passing, you asked why Krishna did not prevent Arjuna from being killed. At this point, Krishna had already left the earth. That is the whole reason why the Pandavas decided to leave the earth as well.