Snag up a 16GB SanDisk SD card or something similar and you're good to go.
The Wii is ... persnickety. I had issues in the past. 4GB or smaller cards may be standard SD, as in non SDHC. That seems to.be the most compatable. That is what existed at launch. SDHC was for cameras. The Ninty drivers were, and still are, crap. Tons of stuff has issues from time to time. I have a 16GB Transcend that was my main card. Worked for everything IIRC. Have a 32GB sandisk now that works although i can't recall if priiloader/bootmii/neek/rawk sd/salty/quadforce or OpenBOR worked with it. Those are all the most picky apps in my experience. 16 gb transcend worked. Class 10 i think.
Try cards. Non SDHC/SDXD are more compatable. Just because the Wii sees it doesn't mean all homebrew will. There used to be a compatability list...
And the Wii formats like shit. Use Panasonic SD Formatter. It was the standard. 32k clusters. GuiFormat should work but didn't exist in the Wii days. Panasonic SD Formatter was the standard. I still use it for old stuff.
Do consider rehacking the Wii and starting from scratch. ModMii is easy and you can eliminate a ton of variables by making sure every cios and app is up to date and correctly installed. It's FAST and easy. Modmii downloads ios files, patches them and gets your homebrew too. Prints a guide. You can skip installing HBC as long as you're sure it's upto date.
That would be the intelligent, complete. easy,no guess-work, preventing issues route.
Having out dated or i incorrectly configured shit is mostly what goes wrong with Wii,... mostly.