I've got the newest version of the ASIO drivers, and I reinstalled them first thing after I first discovered the problem. There's no sound output at all. I'll leave the Cubase mixer open and wait for it to happen again, so I can see if it receives any input.
I've got drivers for the onboard HD sound module installed, although I've disabled them. It uses the RK as standard sound device automatically. I have noticed that it takes a while for the sound to "activate" whenever I open an application as well (as in, this happens all the time, not when the sound dropout problem appears). E.g. after closing Cubase earlier, I opened an mp3 in VLC, and it took 25 seconds before the sound activated.
Edit:
Confirmed. There's neither input nor output when it's in that state. It also seems to make Cubase crash, but if the interface it's using suddenly disappears, I guess that's kind of natural.