I've had this problem with two RX480s and now two computers, one with a fresh Windows install, so I'm pretty sure it's an issue with the drivers, but I don't know if it's widespread:
I have had a reference RX480 since launch, and the card works great in games: no issues to speak of. However, if I leave my computer on and idle for a while, the computer will BSOD and restart. Checking the blue screen log, this results from a THREAD_STUCK_IN_DEVICE_DRIVER error in atikmdag.sys.
I had the issue with my original RX 480 on an i5 2500K and Gigabyte Z68AP-D3 motherboard. After multiple driver reinstalls and cleanings with DDU, I exchanged the card for another one, believing the hardware to be faulty. My second card exhibits the same behavior. As part of the original troubleshooting, I replaced my power supply with a new one (just in case my old supply was potentially the culprit). On Friday, I built a new machine and have a fresh Windows 10 install, so the card is now running on an i7 6700K with MSI Z170A Gaming M5 motherboard. Again, I get the same BSOD error when the computer is left to idle for an extended period of time.
I am currently trying out using Guru3D's clock blocking utility, which prevents the GPU from downclocking to its lowest power state, and while I've only just reinstalled it on the new machine, I ran it for several days on the old machine, and it seemed to prevent the BSODs, leading me to believe there's a problem with the 0 state of the 480 drivers, which may be lowering the voltage of the card too much at very low power saving levels, but that's just speculation.
Is AMD aware of the problem, and is this something that others are experiencing? The ClockBlocker utility is a workaround that may work long term, but it draws extra power from the GPU that I may like to avoid if possible, and it doesn't solve the issue.