Tobi mentioned that Itachi was sick with a disease, and was taking medicine for it to extend his life. This happened right after the battle for Sasuke when he woke up. Tobi told him the truth about Itachi at that time, and the disease and illness was a part of it.
The Wiki notes it on the last line of his Background section, and references Chapter 401:
At some point, Itachi contracted a terminal illness. He kept himself alive through the years with medicine and sheer willpower so that he could live long enough to die by Sasuke's hand.
And it also notes that Itachi's death was actually due to the illness, that the fight between them weakened him enough that he couldn't resist it much longer. That does explain why he lived through Sasuke's Kirin, but then coughed up blood and was unable to do anything else but walk and maintain Susanoo for a minute, and then gave up after saying his last words.
Edit: He did also have enough strength to implant one cast of Amaterasu to go off when he saw a Sharingan (possibly Tobi's specifically, but that was never clarified), which was triggered right before the truth was revealed.