Items/power-ups in Classic Game work differently compared to the Normal Game; they work similarly to past Bomberman games. You keep all power-ups between stages (other than Invincibility) and only lose them when you die. You do keep your # of bombs/firepower/speed if you die though. There is one power-up per stage.

List of what items are on what stage is at the following link: https://bomberman.fandom.com/wiki/Classic_Mode_(Bomberman_Portable)

It follows a similar (but not 100% exact) pattern to NES Bomberman.