There's no setting for that.
The Gamecube doesn't have any auto-shutdown after a fixed amount of time.
If the Wii shut down, it means that DIOS MIOS (Lite) encountered an error. It could be your ISO, or your Setting, or your setup. Try another version of DIOS MIOS (Lite). Try DML if you are using DM to see if it's caused by your USB device.