and they already did a fake out where they make you think he died right away and then they bring him back, just for him to die a month later because...? If that was going to take him out I don't see why it took a whole month lol
The Answer will explain a bit more, but basically, defeating the final boss used up his energy (literally costs all your HP to use the final ability). After that he was holding on for as long as possible to say his farewells to everyone, as well as hoping that SEES would remember in the end. That's why there's descriptions of him getting increasingly tired as the the day goes on.