Macbook shutdown issue

I have an Intel macbook running 10.4.11 and am having a problem with the macbook shutting down on its own.

When using the laptop, everything is fine. But if I leave the computer alone (no typing, no mouse movement, etc) for a minute or two, the screen that pops up when you push the power button (restart, sleep, cancel, shutdown) comes up. If you do not move the mouse within a few seconds or click cancel, the computer turns off.

The computer is not running too hot, and there doesn't seem to be anything else going on strangely with it. It runs fine when it's in constant use; it only has the issue when you let it stand for more than a minute or two.

Any suggestions would be greatly appreciated.