Thanks folks.
I contacted MatterHackers (my reseller), and they said something similar to what SandervG described above. It may have been a faulty part, or I may have just been unlucky and the PLA detatching eventually flooding the print core. I just got the thing a few weeks ago (no mods or non-default settings), and it's been working great before this, so I'm inclined to believe it was just a fluke.
The good news is that they offered to replace the printer, so apart from some downtime it's not a lot of hassle. So despite the issue, I'm very happy with the customer service of MatterHackers and would recommend them to others.