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There are an endless number of power-centric optimizations that could be made. Do you sync the time once an hour, four times a day, once a day, etc? Do you need the clock to always be spot on or are you insensitive to a few minutes drift? Power save scheduler, perhaps you are willing to halt updates outside of an active hours schedule e.g. when sleeping as suggested earlier.
If your Kindle will be serving as a clock at a fixed location one could have a motion detector trigger the clock to update only when someone walks into or is active in a room. The motion detector could drive an electromagnet to trigger the hall effect sensor (same as a smart case).
Are you willing to set the Kindle in a cradle where power use is no longer an issue? And so on. There are scenarios where you might only get 5 or 7 days on battery. And others where a month should be possible. And enough variables that you might as well do some empirical testing to get accurate run time figures.
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