A Series Of Unfortunate Events is not just a morose tale of three orphans trying to escape an evil Count, it's also absurdly hilarious. That humor is the key to making the dreadful tale of the Baudelaire orphans enjoyable, as otherwise it would surely be bogged down in misery. One of the first quirks introduced into the story comes in the form of a nagging cough that never seems to go away. The Vice President in Charge of Orphan Affairs at Mulctuary Money Management in A Series of Unfortunate Events, Mr. Poe, is always coughing, but the series doesn't explain why.
Almost nothing in A Series Of Unfortunate Events is a coincident or accident. While some occurrences may seem random or unexplained, there's always a secret organization or a shady figure with a dastardly motive to explain what really happened. One glaring exception to this rule, however, is Mr. Poe's cough. Lemony Snicket, the detail-oriented narrator of the series, seems to gloss over the ever-present hacking from Mr. Poe. While the Netflix show offers little in the way of clues or hints as to the truth behind Poe's affliction, the A Series Of Unfortunate Events books provide a clue that reveals a little bit more about the banker's illness.
Throughout the release of the 13-book series, Daniel Handler (under his pen name Lemony Snicket) released a few books that dove into the background of the characters that made up the world of ASOUE. One such book, Lemony Snicket: The Unauthorized Autobiography, dedicates an entire chapter to the banker entitled "Why Isn't Mr. Poe As Helpful As He Ought To Be?".
The chapter includes a transcription of a conversation that supposedly happened between Poe and his sister Eleonora (a character that is changed to his wife in the Netflix series) at the restaurant The Anxious Clown. At one point, Eleanora says, "You've had that cough since we were children and it never seems to get better." Mr. Poe quickly responds, "Never mind, Eleanora" and changes the subject. It seems that although Mr. Poe is very aware of his chronic coughing, he would rather not discuss it. It seems that Poe's cough is merely a character tick. Perhaps it's a metaphor, showing that Poe is unfit to be taking care of these Orphans. Or maybe, in this instance, a cough is simply a cough.
The cause of Poe's cough could be many things, from a prominent cold to that sensation of having food stuck in your throat even though you haven't eaten in a while. Harvard attributes a chronic cough, a phrase here which means "cough [lasting more than] three or four weeks", to a variety of possible illnesses including "postnasal drip, asthma, gastroesophageal reflux disease, [and] chronic bronchitis." They also point out that smokers frequently have a chronic cough.
Poe's chronic unwellness is one of many hints, along with his inability to recognize Count Olaf in even the most obvious of costumes, that he should absolutely not be in charge of the Baudelaire orphans. However, just as it is absurd to have a cough for no reason, Lemony Snicket is showing how absurd it is that people as incompetent as Poe are often responsible for the well-being of those who cannot help themselves. It's one cruel joke among many in the Series of Unfortunate Events.