Check all connections to and from graphics card.
-PCI slot(make sure card droop is not creating a poor connection, this is unlikely but the 390 is huge)
-power (make sure both are secure and making good connection)
-HDMI/DVI cords (changes cables if possible could be faulty cable)
Could be software related but what you describe is typical of a dying/overheating graphics card. You can make sure you are not having a driver conflict somewhere by using a driver uninstaller of your choice and reinstall drivers. I use the AMD one, read the warnings.
If the problem persists you can try.
-Is your card overclocked factory or manual? If so, try to see if you have the same issues at stock clocks Core/Mem ~1000/1500.
-You can also try under-clocking the card. Core/Mem ~950/1250 or lower on the core clock. I use MSI afterburner (I own R9390x)
-Are the fans working properly and is the card clean and getting enough air? Have you been monitored your temps at idle and gaming? Thermal paste might be needed to be reapplied (fairly advanced disassembly/reassembly) Overheating can cause these issues.
- Check out the R9 390/390x owners club and search for people that have/had the same issues or ask there. http://www.overclock.net/t/1561704/official-amd-r9-390-390x-owners-club A lot of savvy R9 390 owners there.
If under-clocking works you should also use v-sync or the Chill function in the AMD Radeon settings a FPS limit close to monitors refresh rate. This will keep the card cooler in general.