They don' t need to be cleaned a lot unless you get the feeling they have collected a lot of dirt and grit....if the cases are coming out scratched etc.

Use a cotton ball and a Q-tip with alcohol and clean the die thoroughly and then immediately after cleaning, lube them well so they don' t rust.

Dies are almost exclusively made from 12L14 (leaded) screwstock and casehardeded. This combination will rust quickly if not protected.