QUOTE
I just make my computer go to sleep when I'm done for a period of time, or when I'm done for the day.
OK, but you really should let the computer decide when it wants to go to sleep. You should have learned that with any child you cared for...
I assume by "when I'm done for the day" you mean you either manually Shutdown or you have Energy Saver Shutdown the Mac at the time you designated. Do you use Energy Saver System Pref?
Many don't.
I suppose there should have been a "Case 3:"; "I can't explain it" 
Personally, I think it is an over-sensitive power supply, low voltage on the receptacle, a lees-than-optimum cable or either port (computer or drive).
Do you have another suitable, empty port on the Mac? Is there more than one port on the drive's box? Do you have another cable of the type needed? Are there any high-powered electrical devices nearby (microwave, personal time-travle phone booths, etc.)?
Two miny big words!!
Where are the
Admins when
you need
them?!