He had been ill since the summer of 1996. His body is removed from the forest by Hagrid before the other Acromantula can eat it. His funeral is at dusk the next day.
We know Aragog died on 20 April because we know that it was the day before he was buried. And he was buried the same day as the apparition test, which was scheduled for 21 April. Hagrid said that Aragog died at night in his note asking the trio to attend the burial.