Could be a lot of different things. How old is the drive?
Could be...
1) Hard drive failing
2) Something wrong with USB cord
3) Something wrong with the USB port, the cable connecting the USB ports to motherboard, etc
Quick troubleshooting options:
To troubleshoot 1) Try plugging it into another computer and see if it works fine. If it does, its probably option 3
To troubleshoot 2) Try a different usb cord...
To troubleshoot 3) Try a different usb port... if it works then it's probably something with that specific port. I had this just recently happen to me.
Also a less common problem is that the drive automatically powers down when idle and it could be doing this quickly for some reason. I also had this happen to me. You can temporarily change that by going to Control Panel --> Hardware and Sound --> Power Options --> Change Plan Settings --> Change Advanced Power Settings --> scroll down to the + icon by "USB Selective Suspend Setting" and turn that to disabled.
Do turn that setting back on though because it is helpful for a lot of other things. Just disable temporarily and see if that helps at all. Probably not, it's a weird issue, but it's worked for me before.
P.S. I use a lot of hard drives as a video editor and I feel for ya... they are the most temperamental pieces of blah sometimes.