I am using RT1062 on a custom board. I couldn't find any detailed documentation that describes the SD card interface, so I had to walk through the code to determine what features, etc. needed to be enabled.
To allow the SD card to be mounted, there are a number of conditions that need to be met. Some of them are:
1. SD card must be powered. On the NXP evaluation board, there is a control bit that turns power on.
2. The SD card voltage must be correct. On the NXP evaluation board, there is a control bit that selects one of two voltages. In my design, it is always 3.3V
3. The SD card detect must be active. Most card sockets have a switch that detects if the card is present. This must be wired to the correct pin.
In my case, the code "hung" in an infinite loop waiting for all of the conditions to be met, then eventually timed out. Putting breakpoints in was somewhat tricky because the timer would sometimes time out, so debugging was a long process!
Perhaps the place to start is to look through "sdmcc_config.h" and "sdmcc_config.c" to make sure you have set everything up correctly for your custom board. For example, in the header file, I had to comment out:
#define BOARD_SDMMC_SD_IO_VOLTAGE_CONTROL_TYPE kSD_IOVoltageCtrlByHost
and replace it with
#define BOARD_SDMMC_SD_IO_VOLTAGE_CONTROL_TYPE kSD_IOVoltageCtrlNotSupport
The .c file does some pin assignments, etc.
Hope this helps!