It was a bad game design feature that existed in the Demos as well.
Basically you only had access to the pickaxe during the quest to retrieve it. You needed to have meta knowledge of the quests and know that it was needed in the imp mine and you shouldn't turn it in too early.
At least back during the demo there was a "Collect <something> ore" quest, which basically required you to use the pickaxe in the Imp Mine. If you turned in the pickaxe quest you essentially borked this one.
Luckily, in the product version the walls in the imp mine have the Mithril medium items repair material, which is abundance in the rest of the game, so the pickaxe quest is safe to turn in early.
UPDATE: I have found another pickaxe in