Are you unable to save other types of data (such as Messages), see Save Data troubleshooting. If only the Miis are not saving, please continue.

Go to the Mii channel and create a new Mii (click here for instructions for creating a Mii for the first time or click here for creating a new Mii).

1. Once the Mii is created, verify that it shows up in the Mii plaza.
2. Power off the console, then power it back on and go back to the Mii channel.
3. If the Mii is still there, the console is able to save fine.
4. If the Mii is not there, press the whistle icon to arrange your Miis to verify that it hasn't simply wandered off the screen.

If the Mii is not there, there is likely an issue with the Wii console's system memory, and your system will need to be repaired. Please contact Nintendo Consumer Service to discuss options available to you in this regard.