SD card shield not working on 3.3v
I could not find any info on the full size SD card adaptor, but the microSD adaptor has a 3.3V (LM1117 or equivalent) regulator on it. It, therefore, needs a minimum of 4.5V to operate.

To run the adaptor from 3.3V, you would have to remove the regulator and solder in a piece of wire in its place.