I have problem with my sony hd1000, when i shoot about 20-30mins, after that the picture starts to shake. I have to reboot the camera about 4-5 times and then it is normal again. IS is ON and i have test it also to turn it off.

I have old battery, is that the problem?

I don't see a direct relation between a battery and shaking of the image, think one thing that could cause the image shake is the camera image stabilization that is malfunctioning, as this is not normal behavior and if resetting solves the problem only for a while I would definitely send the camera in for repair.