Can anyone tell me the reason why the shield won't work in this situation?

[Sannda]

I have a problem with the ESP8266 wifi shield and the Arduino Uno Rev 3

I have made it work successfully with either software or hardware serial.
However, if I connect a 12 V power supply to the Arduino and remove the usb cable (connecting the arduino to the pc) the STAT led on the wifi shield just goes off from whichever state it was before (either blinking or continuously on), and the shield becomes functionless. The POWER led remains on though.

In short, the problem is that the shield works either with software or harware serial but only when the usb cable connecting the arduino and the pc is plugged in.