Although the illness of the "red death" that they refer to in the story is more allegorical to the plague, it may also be symbolize any disease that slowly creeps in and ends up overtaking you.
This being said, there are two particular things that seem to creep upon Poe consistently when you look into his life story: The death of his most beloved women to tuberculosis, and his rampant addiction.
Poe was a disturbed man with a high emotional intelligence, as well as a sensitivity for things, that is evident in his ingenious writings. However, he was not a very lucky fellow: Both his mother and his beloved wife died of consumption, leaving him even more wretched than he already was. To self-medicate his pain, Poe was notorious for his consumption of absinthe (way more dangerous then that the newer, commercial versions), and opium, among many other opiates. Therefore, one can assume that the creeping of the red death is no different than the creeping in of the disease of the drink as a result of personal failures.