I recently purchased a WD Passport Studio connected via firewire to a iMac V 10.5.8, The Drive works fine on start up but as soon as the Mac goes to sleep the drive dismounts and the computer has to be restarted to get it to mount again.
If you have a password then remove it, if you don’t have a password then there’s not much to do since it’s something that happens to a lot of computers due to physical design. Waking up a computer does not provide the same power spark as when turning on, some will give enough power and some will not.
My Passport can wake up with one of my computers but not the other ones, same happens to me with a Phantom drive I have.