I took this to an Apple Store. It was determined that the headphone jack was broken.
It was going to cost $199 (if I remember correctly) to replace out of warranty. They don't repair this problem, they essentially charge you for a replacement. The jack is soldered to the circuit board. The unit was only 1 week out of warranty! However, I was told that even if the unit had still been within the warranty period, it would still cost me the same amount to replace, because this particular problem of a broken headphone jack is not covered under the warranty anyway. In Apple's view (according to this Genius), if the headphone jack breaks its the user's fault, because either the unit was exposed to shock (such as dropping) or the unit was stored with the headphone cord plugged into the jack and the cord wrapped around the unit, putting strain on the plug and connector. I informed him that this was indeed not the case, even showed him a separate case I use to store my headphones when I'm not using the iPod Touch. But they still would not bend. I talked to both a Genius and a manager. So I left the store that day without doing anything. On a different day I went to a different Apple Store and talked to a manager who simply replaced the unit for free on the spot as a warranty exchange with no fuss, even though it was a week out of warranty. He said since its only a week out of warranty he would be able to do me the favor of replacing it.
So far, everything's been good with the replacement (knock on wood.) BTW- This is for the 2nd Gen iPod Touch.