This is probably the worst piece of electronics Apple has ever put in their devices. Luckily it's a easy and pretty cheap fix. We sell the part for $19 and install it for an additional $25. However if you know a little bit about electronics you could probably install it yourself.
I think you can also buy the part here though I don't think they install...
[http://www.ipodrefresh.com/iPod-nano-6th-gen-Power/Sleep-Button-Repair.html|iRefresh, ipod nano repair]