Instructions
Turn the system off and back on. When the system turns back on, check to see if the Wii is still shutting off shortly afterward.
Turn the system off and unplug all cords from the back of the console.
Reset the AC adapter by taking apart both ends of the adapter. This means the end going to the wall should be unplugged, along with the end that was going into the Wii console.
Plug all of the cords back into your console and turn it back on. The resetting of the adapter and console should have solved the problem.