iPod battery messed up.

Make arrangements with Apple to have the battery replaced.

Genius Bar Reservation and Apple Support Options - Apple

Batteries - Service and Recycling - Apple

See the second link in my original post. 

There is no such thing as calibrating a battery. Apple used to suggest that, at least once a month, you let the battery drain until the device shut itself off then charged it fully. This was to calibrate the battery sensor in the phone. But Apple stopped recommending that years ago. What you're describing sounds like a failing battery. The only way to fix that is by replacing the battery. 

If you take it to a Apple genius bar(scheduled appointment) they then will deem if the battery will indeed replaced. $79. Or if you call Apple support over the phone. If you choose the option to send in the device it's $79 + $6.95 shipping. They will send out a pre-paid box to send the device in to them. They will replace the battery and send the device back.

Apple is offering a deal on iPhone batteries because people got their knickers in a twist because Apple slowed down phones with aging batteries under certain circumstances in order to keep them from shutting off. Despite the fact it made perfect sense, it became a public relations problem so, Apple cut the price on the battery.

As the iPods were never throttled, it was never an issue.

The batteries are much different that the one's in iPhones. The battery for iPod is much thinner than the ones for the later model iPhone's such as the iPhoneSE, like the one I have. The issues that Apple was having with the batteries only applies to the later model iPhone's. I was inquiring about it yesterday when on the phone with Apple. They will not honor the same battery replacement as they do with later model iPhone's. I would suggest searching for someone local that does battery replacements for phones. Call them and ask if they will do one for a iPod. I just sent my iPod6thgen in to Apple to have the battery replaced.

Why aren’t Apple offering the same replacement battery deal for iPods that are suffering from the same battery degradation and software issues as their iPhones ?

Unfortunately that does not apply to iPod's. The batteries are different.

Unfortunately that does not apply to iPod's. The batteries are different.

Yes, I'm aware of that. Thanks.