Don't want to pee on the barbecue, but it is unlikely to be the ext disk per se. I see that as being a USB device? If so, it should hot swap to its' hearts' content.
However, what MIGHT cheer you up, is that there is probably some minor issue with the USB side of the PC. I did have something similarly frightening with a camera card reader a few months ago. As soon as it was unplugged, (it remains so) things cleared up nicely - and the laptop was then more receptive to updates, etc. etc. So a re run of Windows update might actually work, given a following wind.
Good luck!
Conan
PS it might be that you have a USB "Connected" icon on the task bar. THe correct way to disconnect a USB device, is to right click it and follow your nose from there. I take it that you already do this?