Daveste,
You could replace the 3.3 v regulator, if you like soldering SMT parts, that is.
If you need help finding it, then it is probably beyond the scope of your (present) abilities.
A TO92 LM33 regulator with a .1uf cap on the input, and a 10uf electrolitic cap on the output should run an SD card, but I would check. They can use a lot of current to write.
See the datasheet for the regulator for simple circuits to wire it up.
regulator: http://www.digikey.com/product-detail/en/LP2950-33LPRE3/296-31455-1-ND/3505910
TomJ