2015 Prius C A/C only works when vehicle is moving

You might have ECO mode on. You should see a light on your dash indicating this, but it should still be blowing cold. Just not "as cold". ECO mode will override the HVAC controls and slightly adjust blower speeds etc when the vehicle isn't moving. Likewise it'll keep your car running in the winter if you have the Temp set high.

So see if that light is on. If it is, the button for this is just below & beside the hand brake.

If it's not on, then you have a problem and need to get the system looked at.

 

I have kept the ECO mode on since I bought the car and never had a problem with the A/C. Sometimes I’ve taken naps in my car during lunch break and the A/C never stops blowing cold. I’ve never had the need to set it below 70 degrees even in 100F weather, which is almost all year where I live.

 

Same as iceman13 above my vehicle has been in the eco-mode from its first day of purchase and it is used as a work vehicle that never turns off all day from 6:30 to 7 AM in the morning to 630 to 7 PM in the evening the air conditioning works well parked idling at every stop for 12 hours a day.
I have never came across this problem on a Prius C so if you do you have it repaired at a shop would like to know the outcome and what problems they have found to fix it .