I have the same problem. (see my post - a little more detail)
http://forums.usa.canon.com/t5/PowerShot/SX280-battery-life-shooting-video/m-p/22489 [Mod note- inserted link for convenience of community]
I called Canon and they said they need someone to send in a camera that has this issue to be able to know what's going on. They told me they have the sx280 there and theirs doesn't have the battery issue.
I took mine back and ordered another one in hopes that it will be okay. We'll find out. I do trust that Canon will find a solution but boy what a hassle!
Yes, I will post about my replacement however I won't receive it until next week.
Also I don't believe it's a short battery life issue. It's that the battery icon flashes AS IF it's low when shooting video, when it actually isn't low.
I am not convinced it is solely the battery level sensor. I used the SX280 until, in auto mode, it displayed battery level with one of the diagonal bars missing. I changed to video mode (of course the battery level indicator started flashing red after the mode change) and started shooting a video. After about five seconds of video, I zoomed in to 5X. I got another second or two of video and the camera shut down with a warning to recharge battery. I conjecture that if there was still sufficient battery power, the video should have continued as it does in other scenarios. It just seems that shooting video and zooming the lens puts a very high demand on the battery. If it is not fully charged, the battery cannot handle these demands.