Nope!
To ensure the child's spot, they need to pay the full time rate regardless of attendance.
I just had this scenerio play out with a current client. DCB was gone 2 hours per day, 2 days per week. The rate did not lower. They are charged a weekly rate that is converted into a daily rate, not an hourly rate.
If DCM barks at you about a discount, simply tell her that the rate is not based on attendance, it is based on the weekly spot. If she's not happy paying the weekly rate, you can change her to hourly, however it goes up significantly.
Example: You charge $150 per week...$30 a day. Say the child will be attending a total of 37 hours versus 45. She wants to save money but paying hourly ($5), will actually increase her weekly rate to $185.00. See how that works!
Full time rates are cheaper than part time. Tell her that and you shouldn't have to discuss money with her again.