I've been experimenting with wired remote photography lately, and have been plagued by the Auto Power Off feature. The camera shuts itself down before I have chance to capture anything.
In the Auto Focus mode...this can be overcome, by repeatedly half-pressing the shutter button on the remote, which refocuses the camera and restarts the shut-down timer. This technique is unreliable in the Manual Focus mode.
I searched the manual to see if there was a way to overide the Auto Power Off mode and there is: simply plug in the AV Out Mono cable into the jack in the back of the camera and let the cable hang loose from the tripod. This disables Auto Power Off feature and the camera will remain on until the battery runs out. I would be willing to bet that this works on other Sony cameras as well.