I have ASUS STRIX RX480 8GB and I'm also having the same problem. It only started a few drivers back.
When playing it works, but when I leave my PC on for a few time like downloading a game, windows gives a BSOD and restarts then windows report "Wattman has been restored to default due to an error".
I also have stock clocks and only OC it when gaming to the factory Asus Strix RX480 OC mode.
WHEN IDLE I ALWAYS HAVE STOCK CLOCKS...
ps: I have used the report form on AMD support, everyone do the same and maybe they will think on fixing since I have only had a very bad experience with my RX480, next GPU I will only chose Nvidia even if I have to pay +50€ (never got a single problem with my old GTX570 which is still fully working).
Uninstall MSI Afterburner.