Why does Rolf stop reporting, put his camera down, and just stay with Azucena toward the end of the story?
Rolf puts his camera down, stops reporting, and just stays with Azucena towards the end of the story because he knows that he can do no more for the little girl. Essentially, by this point of the story, Rolf has come to accept the inevitable and that, bar some miracle, Azucena will die.
Since no one has been able to procure the pump that might possibly save Azucena's life, the little girl must be made as comfortable as possible in the last moments of her life. Rolf chooses to stop reporting and to concentrate all his efforts on providing her the emotional support she needs to face death. So, when Azucena laments that no boy has ever loved her, Rolf comforts her with the assertion that he loves her more than he loves his own mother, sister, lover, and any other woman who has slept in his arms.
Rolf stays with Azucena all throughout her last moments, and when she dies, he closes her eyelids, hugs her to his chest briefly, and then lets her sink down into the mud. Throughout the whole ordeal, Rolf prays that death will come quickly for Azucena, as "such pain cannot be borne" indefinitely. Azucena dies with Rolf by her side, as her friend and ally.