Hi Luke,
we're reliant on you to help diagnose that! can you please check the GPIO line when the card is inserted, by using the gpio kernel module (use 3.4 it's easier) flipping it to input and reading the entry? it could be that the manual-soldering of the mmc card slot was done poorly.
I don't have the schematic and layout, so I'm not really sure where I'm supposed to be looking on the PCB. Any clues?
Ryan