STM32F4: SD-Card using FatFs and USB fails
I resolved the problem:

In usb_cdc_if.c the #define APP_RX_DATA_SIZE was set to 4 (for some unknown reason). As this is lower than the packet size 64, incoming packets of a larger size than 4 bytes were overwriting my memory. 

It happened, that the following portion of my memory was the FATFS* FatFs[] pointer-list to the initialized FATFS-Filesystem structs.

So subsequently the address to this struct was overwritten, when a command of 5 or more bytes arrived.

Phew, that was a tough one.