Napoleon was not dying..... he was merely drunk, suffering through his first experience with alcohol. Orwell doesn't need to explain it, he leaves us to infer the cause.
It was a few days later than this that the pigs came upon a case of whisky in the cellars of the farmhouse. It had been overlooked at the time when the house was first occupied. That night there came from the farmhouse the sound of loud singing, in which, to everyone's surprise, the strains of Beasts of England were mixed up. At about half past nine Napoleon, wearing an old bowler hat of Mr. Jones's, was distinctly seen to emerge from the back door, gallop rapidly round the yard, and disappear indoors again. But in the morning a deep silence hung over the farmhouse. Not a pig appeared to be stirring. It was nearly nine o'clock when Squealer made his appearance, walking slowly and dejectedly, his eyes dull, his tail hanging limply behind him, and with every appearance of being seriously ill. He called the animals together and told them that he had a terrible piece of news to impart. Comrade Napoleon was dying!