How can I keep my shower caddy from slipping?

https://www.instructables.com/id/Sticking-Suction-Cups-to-some-Non-Smooth-Surface/

Zip tie it to the shower head arm.

Some people install a second shower curtain rod next to the wall inside the shower and use S hooks to put in their necessary cleaning products. You can hang all you need for the family without it over crowding. Also, there are shower curtains that include pockets in them that allow for use inside the shower. I assume they have holes to let water drain out as the caddies have too. Hope one of these ideas helps, Pam

Command hooks makes a hook that is really waterproof.

If you have hard water, it makes the surface a bit slimy. And if by plastic discs, you mean suctions: Try apple cider vinegar on the wall and suction cup and let it dry. Use a few drops of water on the suction cups to reapply it to the wall.