Okay, three things:
first: my complete embarassment and apologies – the drive is powered via a DC adaptor – I was completely overrun with errands so I unfortunately mistook the drive for another portable that I also have from the same company, which is powered only via USB. So the power supply can't be an issue.
second: I can't find the diagnostic software for the drive on the company's website. It is a Toshiba CANVIO 3tb drive. When I check, there's only Documentation to be found. I tried to install a portable drive application that Toshiba sends packaged with all of the drives and which contains mostly backup utilities, but it wouldn't install (always says that it can't find autorun.exe or install.exe). Since the drive is ext4, I tried to install it via sambashare, but I wouldn't even know how to install it in a proper windows environment, since it doesn't recognise ext4 partitions.
third: when I looked at the model of the hard drive on the Toshiba site, I got a scare in customer reviews - almost all of them negative and complaining of hard drive failure
So it being a Linux partition that windows doesn't really care about, I don't know how to properly check the drive, except with fsck. SMART doesn't work because of the usb connection (counter-logging isn't supported or something like that).