How do you obtain Purple Magic Powder?

It's not failing. RedRaven16; is right. Whether you consider getting a powder instead of what you wanted as failure is of no consequence to the game. Failure, from the game's perspective, is only when you fail to make anything at all. For level 4 items and higher, there's a 90% chance of making the first target item, the only one displayed, the plate/gem/oil, while there's a 10% chance of making the second target item, which is hidden, which is the corresponding color powder. There was never any chance of failure for mining or herbalism.

Um... I dont think it begin at lv 4 items. It's lv 3 where you can make blue powders from steel / sapphire ores and rosemary seeds / flowers.