Fushigi no Dungeon: Fuurai no Shiren DS
This game is titled Mystery Dungeon: Shiren The Wanderer in North America, Europe, and Australia, and Fushigi no Dungeon: Fuurai no Shiren DS in Japan.
Successfully complete the game. Ask one of the blacksmiths in a town to upgrade your pickaxe. Leave it with him, then return after an adventure to retrieve it. Your upgraded pickaxe cannot break.
Strategy guides from GameFAQs