If the additional delay is being added at the point(s) in the cycle where water heating could take place, there could be a problem with the thermistor (see the following link) which relates the water temperature to the control, a problem with the unit heating or a problem with the control.
LINK > KitchenAid KUDI01ILWH2 Thermistor
Can you determine if the heater element ever operates?
Dan O.
www.Appliance411.com
The Appliance Information Site
=D~~~~~~