Problems downloading photos from camera

Hi there! I hope you can help me!
When I hook my camera up to my computer to download the images, the camera always powers off before all of the images are downloaded. I've tried fully charging the battery before downloading the images, but that only works some of the time. For example, most recently, I was unable to get the last 2 pictures from an event off of my camera b/c the camera kept turning off and powering off. Is it the camera? The battery? The cord that is used to transfer the images?

Please help!
Thanks :)