Short version: I have 2 Wii Us. The first Gamepad has severe limitations where it will work. The second Gamepad works everywhere but the farthest rooms of my house. Thus, either the first Gamepad was defective or there is simply a large variance in working range among Gamepads.
Long version: I got a launch day Wii U from Target, and also had a Best Buy preorder shipped to my house as insurance, in case I couldn't get one at launch. My Target Gamepad worked perfectly fine within the room the Wii U was in. It also worked fine in the adjacent room 15ft away, with a line of sight between the Gamepad and console through the doorway. Simply turning my back to the console would trigger the "unstable connection" warning, while closing the door(which is just a standard hollow interior door) or walking out of sight behind the wall dropped the connection. It wouldn't connect at all anywhere else in house.
My Best Buy preorder, which I intended to return since I got my launch-day unit, arrived yesterday. Out of curiosity, I decided to pair the new Best Buy Gamepad with my already hooked-up Target Wii U to see if my results would be any better. It was! I could use it anywhere in the adjacent room with the door closed, and more importantly I could use it all the way in my upstairs bedroom. It only failed to reach the farthest rooms on the opposite side of my house, on either floor.
I didn't notice any posts in here, where people had 2 different Gamepads to test. So, if my experience is any indication, people with poor Gamepad range/penetration might find your Gamepads at fault, and I would try to find a way to test out another 1 or 2 before accepting that you'll never get a good working range within your particular living space.