Internal drives are signalled by the OS or the BIOS to shut down after whatever time you set. External drives aren't directly connected to the system's BIOS, so power management can't function unless specifically programmed into a device driver for the external controller. External drives all use a generic device driver, so it can't assume that your device can be powered down. If the PC is shut down, the external device doesn't care, as its own controller is still powered; just like a printer doesn't turn off just because your PC is turned off.
Most people don't use external drives except for certain activities, due to the much higher latencies and lower transfer rates, so they're turned off except when in active use. If you only use it for backups, why would you leave it turned on all the time?
An external drive is a better backup device because you can take the drive away from the machine you're backing up, for safekeeping. You probably don't do that though, so an internal drive would work just as well, except that if something happens to damage your main drive, it could very well destroy an internal backup drive as well. If you still want portability, you can get removable drive enclosures (nest devices) which connect to the IDE controller and you can remove the drive (hot swap is only supported with certain enclosures and controller cards; standard onboard controllers won't let you do this). You can even get one that uses IDE connections when in your computer, then connects with USB2.0 with a special cable when you're on another machine.
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