The internal power supply requires the voltage from the power pack to be above a certain limit. When the voltage drops below this limit, the internal power supply signals an error to the logic board and begins to flash the 'power' light until the condition is corrected.
Some common causes of this symptom are: brownouts, custom-made battery packs with insufficient voltage or low battery power, or attempting to run the IIc from an automobile cigarette lighter while the car is running. Although the Apple IIc Reference manual states that the Apple IIc internal power supply requirements are from between 9 and 20 volts, anything below approximately 12.5 volts may cause the 'power' light to flash.
CURES:
#1: Verify that the power source is providing the correct voltage to the Apple IIc.
#2: Replace the external power supply.
#3: Replace the internal power supply
If problems still continue then refer to the Apple IIc General Troubleshooting procedures.