Dolphin defaults back to emulated Wiimote despite having set for a real one.

Retrobat keeps changing the Wiimote setting to emulated even though I have it set to use a real Wiimote in the Retrobat settings under the individual system settings for the Wii.

First, hello. It's always a good point to start.

Then, the change have to be done from the RetroBat menu, not from the emulator itself.
That's why it's always revert

That's what I did, I have it set to Real in Retrobat but when I open the emulator it still comes up as Emulated.

I guess you've set it up at game level for the game you launch.
Or you've disabled autoconfig in retrobat

I got around my issue by disabling autoconfigure controls for the system and set it in the emulator itself. Pretty weird that it kept defaulting to Emulated even though I set it to Real in Retrobat....

But why doing that ? It makes no sense as the feature exist in Retrobat...
Have you checked if you have a per-game setting, as advised earlier ?

Nope, I don't have a separate configuration for that one game. I originally tried switching it to Emulated in Retrobat to see if an update switched them but it still stayed as Emulated in the emulator itself so the only way I could fix it was by disabling Autoconfigure controls for the Wii.