Was the Mii created on the Wii console you are trying to edit it on? Miis imported from other Wii consoles cannot be edited.
Are you selecting "Save and Quit" when finished editing? If not, no edits will be saved.
Go to the Mii Channel and create a new Mii (click here here for instructions for creating a Mii for the first time or click here for creating a new Mii).
© 2018 Nintendo.