Tod ballet flats are part of my run-around uniform.
I wear them all the time and the little rubber pebbles hold up pretty well. So far I haven't had to do anything with them yet, but I was told at the Tod NY store that they don't resole with those things for you. You can however get a regular sole put on by, say, Shoe Service Plus, and it should look fine. I've never done this so don't know for sure.
So I deal with it by buying lots of them and rotating them to prevent too much wear and tear.