Repost from another thread:
Yeah, yeah, same problem here. My nano is 1.5 years old, so the apple store people said there is nothing they could do except offer to sell me a refurbished one for $95....ripoff. A new one would cost me $129. I am disappointed that apple would not have some sort of special repair program in place for this obvious design flaw. As Roberto pointed out on his website (see more below), this problem is caused by a shim that slips to the side because it is held in place by a tiny piece of double back tape....lame design flaw!
Anyhoo...I don't expect apple to care about me even though I own three iPods, two high end iMacs, and three iPhones. Instead, I found a website that explained the problem. Then I followed some instructions on YouTube showing me how to open up the iPod. Putting these various information sources together, I opened mine up and was able to fix the problem in about 20 minutes. It takes some careful work and some small tools, but it is doable. I did not glue the shim back in place because I am lazy. I just shifted it back into position over the sticky tape and pressed down on it. Hopefully it will not slip sideways again for a couple years. I will also make a point in the future to push this button squarely in the center rather than on one of the sides...pushing the side of the button gradually squeezes the shim out of place. I used a tiny metal screw driver instead of the plastic tools that people show in the YouTube videos, so I sorta scratched the edge of the screen a little, but no big deal for me. Also the mini pieces of tape around the inside edge of the nano are really tough to get back perfectly in place. Whatever...It works now.
Roberto's website is http://www.rbarrios.com/projects/NANO6BUTTON/
You can find many disassemble videos on YouTube if you search for "iPod 6th gen repair screen."
Good luck!