This is such a common problem yet it has no common resolution. Instead, there are dozens of possible solutions and it is up to the users to figure out which works for them. If any do.
Sadly, USB 2.0 was supposed to fix this. It didn't. Then USB 3.0 was supposed to fix it. It didn't. :banghead:
For this reason, I avoid and don't recommend the use of USB external drives.
I avoided the problem by going with eSATA instead of USB for my external drive docking station. But that really was not good because it required the "host" computer be up and running in order for me to access the drive from my other networked computers. Plus, not all motherboards support eSATA.
So my solution was to repurpose my old XP system as a NAS and I recommend folks with perfectly good XP systems sitting around do this (or get a NAS instead of a USB external drive).
By disconnecting the power cable from the drive and re-powering up the drive it appears fine.
That suggests to me a USB timing issue during the boot process and I don't know a solution for that - especially since you indicated this device has its own external power supply.
What others have done when no solution was found is to convert their external drive into a NAS with a
USB to NAS adapter. To me, the biggest advantage a NAS provides over an external drive is that it hangs off your network, not a host computer. So any computer on your network can access it without a host computer being up and running, AND without needing to open up sharing on the host computer either.
Another advantage is the NAS can sit in another part of your house. I have a client who's house was robbed and the badguys took his computer and his attached external drive which contained the only copies of many of his digital family photos and other files.
If the NAS were in another part of his house the burglars may not have taken it.