Maybe too late because Surface Pro 2 Windows 10 will not have Microsoft support from Oct/2025.
I had this issue for a week. I tried all the tricks above. None worked.
It started when I store the Surface Pro 2 in my car for some hours. When I brought back the unit at home, it started to fail.
I tried for the whole week, sweating. I got tired and turned the temperature down of the room and it worked.
I though it was lucky, so I turned the temperature up again. The next day, it didn't work.
I turned down the temperature, put the Surface Pro 2 in front of the air conditioner for 10 min, and it started to work again!!
I guess the temperature helps to improve the connectivity.