Actually it's been my experience that when a trackball is too clean it skips and slides instead of rolling properly. Trackballs end up coated with skin oil after use so it's my belief that their designed to use it as a lubricant.
With my computer trackballs, I'll rub the ball between my palms to re-oil them after cleaning. Makes a huge difference in how well the ball rolls.
You'd have to disassemble an arcade trackball to do that, so you might just want to play a few trackball games to get the ball oiled up and rolling properly.