Sounds like a coding or initialization issue.
Perhaps timing different without the debugger, or the debugger initializes something you later depend on.
If BOOT0 pin floats the chip may not start reliably.
No idea about your code, board, or STM32
Anecdotal descriptions are hard to diagnose.
With SDIO/SDMMC implementations with FATFS, start by debugging the low level DISKIO layer, failure at the top-level/application won't identify a cause.
