Are you using File Patch Code v3.5.1b (and not any other version of the file patch code)?
If you are and the problem persists you may be encountering the read errors I mentioned when using more than 1.95GB of SD data with Dolphin (
https://bugs.dolphin-emu.org/issues/8823).
The best way to get SDHC support in Dolphin is to draw attention to the above issue on the
Dolphin emulator forums. I want SDHC support too but developers must have interest in adding it.
Update: We now have
SDHC support!