I'm not a fan of USB powered drives - far better to have a mains powered one.
As people tend to jiggle USB plus when installing and removing them that can cause solder joint failures on the connector which could manifest as a problem after a period of use and things heat up, and could also be responsible for the drive disappearing.
Tip: use a short USB cable (6" long) to plug into rather than the port on your pc. Cheaper to fix than a motherboard...
Bear in mind too that this is an OLD issue AND affects Mac and Linux users too so best to look for a common factor.
Power settings are a red herring as they aren't relevant while transferring data, only when idle.
One thing to check (as per the old days) is for IRQ conflicts - check under device manager / drive controller.
It's best for drives to have a dedicated IRQ rather than share it, and this has and definitely can cause issues.
There was a case where an audio device shared an IRQ with a HDD and the HDD kept disappearing. Switched to a different IRQ and bye-bye problem.