I am deciding whether or not to buy a Kindle with "special offers" to save money, or without. I am wondering if these decrease the battery life and how significant the decrease is.
For Kindles that use E Ink displays:
E Ink's technology is commonly referred to as "bistable". What does this mean? Bistable means that the image on an E Ink screen will be retained even when all power sources are removed. In practice, this means that the display is consuming power only when something is changing. For example, when reading on an eReader, power is only needed when turning to a new page but no power is consumed by the display while reading the page. This is most noticeable when an eReader goes into sleep mode yet there is still an image being displayed. By contrast, with a traditional LCD, the display is needs to be refreshed around 30X per second, regardless of the whether anything new is being displayed. Bistability significantly reduces the power consumption of displays using E Ink and is a key reason eReaders have such long battery life.
The "Special Offers" do change the screen and therefore cost a small amount of battery when the Kindle goes to sleep. But Kindles without the ads also change the screen when going to the lock screen. Depending on the exact nature of the image, it might be more or less expensive in terms of battery than whatever ad you might have received.
For Kindle Fires, the ads are run on the lock screen and not when in sleep mode. Again, the difference is just which image is displayed so the energy cost differential should be negligible.
New ads for both platforms must be downloaded occasionally to replace the outdated ones stored somewhere on the device. But the device only checks for new ads when you sync up, so there's no extra network connections being made. I've left my WiFi connection off for weeks at a time and the ads just age out and go to a generic screensaver. As soon as I sync, I start seeing new ads. The device does not turn on a wireless connection unless you command it to.
In sum, battery life shouldn't be a concern one way or another when deciding which configuration to buy.
I have a Kindle Fire HD, changed the ROM several times. Now I'm back with the Stock ROM and didn't notice any change in battery life. In fact, my Kindle is running for almost a week (I read before going to bed) and it still have 30%+ of battery life left.
To be honest, I don't care too much about them. So if the price difference is significant, go fot it. There's some ways to disable them, though they might be illegal to cite here (?)