Fish can die from bullying after a week or months, it depends on the health and size of the fish being picked on and whether it gets any food and how much stress it is under. In a massive tank with loads of hiding places, a fish could live for months to a year or more while being picked on. But in a small tank with loads of bullies and nowhere to hide, the victim could die in a week or two.
With discus it tends to be a month or two while the victim slowly gets weaker and then eventually gives up. When that happens, they stop eating, roll over and die.