I've had 2 USB HDD's fail on me in the past. Both due to HDD failure (the USB enclosure is still working; verified by plugging the HDD into another computer).
100% of my failures have been due to accidently dropping the drive, having it fall off a table, having the cable wrenched out at unexpected times, etc. Basically, my own negligence and stupidity.
I fixed this problem by taking the HDD out of the USB enclosure and connecting it via the internal SATA interface in my home media PC. There have been zero failures over an equal period of time since I took me out of the equation!
Remote backups are done via a remote backup service over the Internet.