My first complaint about the S110

Do you have anything else enabled that may be draining the battery such as GPS and GPS logging. I shut them off unless needed. I also turn off Continuous autofocus for general photo-taking and use Shoot Only instead. Continuous AF is the default for video so it will go on automatically when you begin shooting video.

I've also read that with more use, a new battery will hold it's power longer. So let the battery run down and fully recharge it a couple of times. Do not take the battery out of the charger until the green light comes on.

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