I don't mean to spam this thread with what might be an unrelated issue to the OP, but I wanted to give an update. I bought yet another Belkin USB3.1 C to C, and it didn't help at all. Today I had the same issue, and now that I have three cables to play with I've done some more experimenting. It seems that the random shutdown issue lies with the left side ports on the laptop itself, and seems that it might depend on heat, as it worked fine earlier this morning and then randomly shut down and refuses to work now, while the right side ports work fine. Even directly plugging in my external HDD to the left side ports is now not working. I suppose I'll be talking to support about getting the ports checked out somehow.
Anyone have any experience with this?