Some tech companies such as Google may be prone to disabling their smart thermostats as soon as the warranties expire, but Amazon makes sure your older devices continue to function long after the point where they belong in a museum.
in late September 2019 Amazon sent out an email to owners of older Kindle models, advising them that their device needs to be updated to continue to function. I didn't get one of these emails, but someone over at MobileRead did:
We're contacting you regarding your Kindle Keyboard (2010). If you have not yet completed the most recent update on your Kindle Keyboard (2010), please do so prior to October 1, 2019 or you will be unable to use the Kindle services on your device. The update ensures that your device remains up-to-date with continuously evolving industry web standards. After October 1, you’ll need to update your device before you can connect to the Kindle services.
How to Update
Connect your device to WiFi and the update will automatically download and install on your Kindle. For more information on how to download and install the update for your Kindle Keyboard (2010), visit www.amazon.co.uk/help/ku-2019
Alternatively, you can manually install the software update by downloading the update to your computer and transferring it to your Kindle. Visit www.amazon.co.uk/help/ku-2019-manual for instructions.
Note: If your device is already up-to-date, or if it is not listed on the above page, no further action is needed.
This looks like a repeat of 2016, when Amazon released a small but critical update for older Kindle models. That update was mandatory in order to guarantee that the devices could continue to work with Amazon's wireless service, and from what I read over at MR, the same might be true for this update.
So if you're still using an older Kindle model, you should definitely check to see if you need to update.
Here's the link Amazon provided for the page of affected models:
That page includes instructions on how to check which firmware your Kindle is running, and how to install the update.