So I recently bought an Gigabyte R9 390 Gaming G1 and I've been receiving this issue frequently. It happens when under load (e.g. playing games). I've update and reinstalled drivers - hell, I went as far as reinstalling the OS *and* moving from Windows 10 back to Windows 7. I've tried replicating the issue through benchmark software, but I've only managed to achieve the issue while playing games. Namely The Witcher 3 and MechWarrior Online. It does not appear to be a heat related issue as temps when the drivers crash can be relatively low (52*C) and stress test via benchmarks have maintained much higher levels of heat than I've ever achieved in games.
The card has not been overclocked past factory settings.
Operating System: Windows 7 Ultimate 64-bit
CPU: Intel Core i5 4690K @ 3.50GHz
RAM: 16.0GB Dual-Channel DDR3 @ 931MHz
Motherboard: ASRock Z97 Anniversary
Graphics: AMD Radeon R9 390 Series
PSU: Antec VP600P 600w
Thanks for your help!