We use a sitter twice a week on the days that DH and I both work I am part time.
We will he going away for a little over a week for a mandatory family destination wedding so we would not need her for 3 days. With our other sitters, they never asked to be paid for the days we didn't need them. She didn't demand that we pay her. But she did ask if we were planning to even if it was half the rate.
If she worked for us full time, I would understand doing paid days off but i didn't know what people normally did for part time sitters. We are also very understanding of her schedule and if there are days that she can't come, we accomodate that.