Maybe I'm doing something wrong but when I tried playing Mega Man: The Power Battle, I could not map the weapon select button. The input was also not available leaving the controls at the default mapping. I loaded the Japanese Rockman version of the game and it had the same issue.
I played the game via Retroarch/Final Burn Neo to make sure I wasn't going crazy imagining a third button, but the weapon select input did work there.
The games were acquired via update all. Not sure how long this issue has been present since it's the first time I tried to play the game.