Disclosure: I do not have an iPod, and so this may not apply to your device.
Soft buttons on many devices, such as cell phones, remote controls, etc. are made of a piece of shaped silicone rubber with a graphite-impregnated pad on the underside of the button. This pad touches a corresponding pair of copper contacts on the circuit board, closing the circuit with the graphite.
Over time, the surface of the contact pad becomes dirty, and no longer conducts electricity,even when you push the button hard.
Open the device, and carefully clean the silicone-graphite contact pads, as well as the copper contacts, with a Q-tip slightly moistened with rubbing alcohol. Don't use too much liquid, since you don't want it running over everything. This will help remove accumulated dust and oil.
If this does not work, you may have to use a knife blade to lightly scrape the silicone-graphite pad surface, exposing fresh material. Do this carefully, since it is easy to cut too much.