Also known as the 'Weakening Deaths', or 'The Curse'. It only affects men past their late 20's in a relationship that has a problem. Symptoms include nightmares that cannot be remembered and an inability to get any rest. If the victim dies while having the nightmare, they die in real life, their body undergoing severe atrophy that cannot be linked to any natural cause. It is said these corpses are the sources of the ants that have been seen.
In reality, the Weakening Deaths are caused by the Great Trials, a large tower of blocks built by Dumuzid and orchestrated by Astaroth. Each night after a victim is chosen by Dumuzid, they are forced to climb up multiple floors, making a pathway by pushing and pulling blocks. If they fail, they fall to their death, and wither away in real life with a look of agony. Also, as seen with not only Vincent but the bar patrons he helps, as part of the final trial of every night, a victim must outrace a fearsome and gigantic monster representing one of his fears or sorrows. (Vincent's changes every night, taking various forms, including Katherine, Catherine and himself, but the ones that the bar patrons face are the same each night.) Since in the past 700 years there have only been 3 documented men who have completed the Great Trials, most men who are inflicted with the curse die.
The purpose of the Trials is to separate men from fertile women they have no intention of procreating and starting a family with. Given a woman reaches the peak of her fertility around age 27, this explains the ages of most of the victims. Men who are uncommitted to their lover but still stay with them are holding back the future of the species, as Astaroth sees it. In addition to inflicting Nightmares, Dumuzid also employs the services of a shape-shifting succubus (Catherine) to end the relationships with an appropriately messy affair.
Many characters make reference to this curse: specifically Justin Bailey, who is researching it for his own purposes, and Erica Anderson, who just likes spreading rumors. Though the rumors surrounding the deaths have them occur in cycles of 100 years, this is not completely true, as Dumuzid made reference to causing the birth of Vincent Brooks by splitting his mother and her lover apart, so she could start a family with someone else.
By watching the news reports every day at the Stray Sheep, you can keep up on what lives the 'curse' has claimed.