After abandoning the project for a while and redoing the electrical architecture of my board, I found the issue.

Part of the code for the SDIO / FATFS was being auto-generated by the STM32CubeIDE (handy tool, but not bug free).

When setting up the FATFS, it was requiring me to use a "Card Detected" pin. For my board, this pin collides with the SDIO D3 pin. So, I was forcing one of the SD Card data pins to ground (although operaitng it in 1 bit). Thus, I was getting intermittent behavior.

I removed this part of the code + removed totally this card detected pin, subtituting it by a software logic and leaaving the GPIO uninitialized. Now, it works like a charm!