I nad exactly same problems with my new / fully patched Surface Pro 3: miniSD Card not working / not recognized. Solution mentioned ealier worked.
So, the exact steps below:
- Open "Device Manager" and find non recognized device in "Other devices"
- Righht-Click and use option "Update Driver Software..."
- "Browse my computer...."
- "Let me pick from a list ...."
- from the list fine and click on "SD host adapters"
6) Choose the last one: "USB Mass Storage Device" - do not choose any "Related USB Card Reader devices"
... and SD Card should work from now.
Why Microsoft didn't publish such list for the last several months I could not imagine. Surface 3 is wonderful device with only minor problems, that could be easily addressed.