I had the same thought to clean the contacts on both the computer and the docking station when I read that comment about reversing the docking cable.
However I ended up using alcohol and a "q-tip".
I powered down the computer and unplugged the dock. I then used some 99% iso-propyl with a special q-tip type cleaner.
Seeing as I couldn't connect to any docking station around me, I think it was the contacts on the Surface Pro, not the docking station.
I guess it isn't that much of a surprise as it goes into and out of my backpack 2 to 3 times a day. Probably just some dust or other garbage got stuck on one of the many metal contacts in there.
Good Luck!