Electronic – SD card SPI interface for PIC18F25k80

The SD memory specification version 1.01 states an operational voltage of 3.1 to 3.5V so you're outside that range. Also the specification allows up to 50mA to be drawn over a 400uS period and peaks can be higher, so unless you have a sufficently sized capacitor to act as a reservoir during those peaks you may have small dips on the power supply causing a processor reset.

It could also be a software issue causing a watchdog reset or other undefined condition if the SD card isn't responding as expected due to being operated outside the specified range. Either way it would certainly be worth getting to the bottom of your power supply issues.

You may Refer to following link, it's for PIC24 but procedure may be same for PIC18 to use Microchip application libraries:

http://www.engscope.com/pic24-tutorial/14-3-setting-up-the-usb-framework/