I've had this problem before with a bad rom once OP. Did it start when you put a particular game on it? Take that game off. Mine was a bad rom of Cave Story. Whenever that rom was selected on the list of the Sky3ds, the card would completely stop working. No light, nothing. I popped it out, put it back in nothing. Pushed the button, nothing. I had to take the rom off to make it start working again. If you don't know exactly which one it is, take off the ones which you added before it started acting up. Put them back on one by one to see which one was the bad rom.
This was the case when my Sky3ds seemed to stop working.