I've had this happen to me before, it's just an error that can be randomly triggered. I noticed it mainly happens when I play around with the buttons when the screen fades to black after you select the game on the Wii menu. There are other triggers however. If you press the buttons repeatilly during the "broken" state, it turns back on faster. I have no idea exactly how this happens though.
Happened to me when the batteries were low. There's probably some loose wires or somethin'- specifically, between the battery and the rest of the Wiimote.