Have had my Surface 3 for about a week. Installed a new Samsung EVO 128gb card and am having the same problem. Tried, tape, format both exFat and NTFS, changed policy with no luck.
Chatted online with MS tech support. From shut down they had me do what they called a Forced Restart, holding down the power button and volume up button at the same time. The tech assured me that would fix the problem and, of course, it didn't.
A second chat with them and they offered to replace the Surface. This card worked on my Dell laptop with an SD card adapter with no issues. It would seem that this is an issue with the Surface hardware but it also seems doubtful that a new one will fix the problem. Despite liking the Surface I am leaning towards getting something other than a Surface.