Why couldn't the doctor save River Song?

Answer 1

He could have, by completing the circuit himself in "Forest of the Dead," which would have resulted in his permanent death. In fact, he wanted to complete the circuit which would have brought back the 4024 people saved by the Library computers (including Donna Noble and Miss Evangelista), but River Song refused to let him, saying that if he died in his tenth form they would have met, or had any of their adventures, which refused to allow. To prevent him from dying, she knocked him unconscious and handcuffed him to a pole, in favor of completing the circuit herself. The Doctor exclaimed, "I can change this! Time can be rewritten!" to which she replied, "Not those times-not one line, don't you dare," and activated the circuit, bringing back the 4024 people saved in the Library, but resulting in her death.