I guess your Disk has a separate power supply? Is your Disk rotating if you only plug in power, but not USB? Does it go to standby in this case? Your Host can't handle the disks power modes anymore, if it is shutdown.
You can try to disable powering the USB Ports, when the Host is powered off, but you may lose the ability to start your Host by Keyboard. This option you can find in the BIOS if you're lucky.
Maybe an update to the disks/controllers firmware may help you.
Or you can try some Master/Slave socket, that cuts the power of the disk automatically, when the Host is off.
Holger