She died because she wanted. In animé she says that she is alive and wants to die to full became heroic spirit. She doesn't want to be betrayed, again, par her own people...
She wanted to die but she couldn't because she had Avalon within her. Than she completed contract with Holy Grail War. She competed with the master Emiya Kiritsugu. After war, when Kiritsugu found Shiro, he saw the poor boy was going to die, so he put Saber's Avalon within him. Saber returned to her real life it didn't pass seconde she was summoned again par Shiro. For her the time was La Reine des Neiges in her real life. She thought:...