Is there any way to solve such issue:
"Display driver amdkmdap stopped responding and has successfully recovered" - ID 4101
The same happens to people with Nvidia drivers, so it's for sure not Nvidia or AMD fault.
Last time the issue happens 3 times in a row when I was fighting with enemy, I asked last blow and bah, Game not responding and Display driver amdkmdap stopped responding and has successfully recovered.
It always happens when I'm playing, not in any of menus. GPU / CPU frequencies are default. Hardware coursor is off (on on it also crashed), vsync off, i tried to limit FPS to 60 / unlimited - without effect. The same thing happens in fullscreen mode, border window mode.
I'm launching game with GOG Galaxy client. I tried also changing priority do high.
The same things happens on 1.02 and 1.03

I tried to set lower GPU frequency (-10%) - without changes, game still crashes.
Maximum GPU temperature playing The Witcher 3 was: 73°C
Maximum CPU cores temperature was 60°C
I played GTA V with overclocked GPU and CPU, with much higher temperatures, without any crash, much longer than W3.

Asus Strix R9 285
i5 2500k @ 3.3GHz
8 GB DDR3
Antec VP 500 (Overall power taken by pc is less than 400W for sure)

This is a problem specific to the R9 285. Check my thread on the CDProjekt forums (this one won't let me link) to see how many other examples are there.
Unfortunately, we have yet to find a solution for this.

Can't say it is the same thing for sure but an ancient problem with the video driver crashing is due to failing hardware that goes for both ati and nvidia cards. Some games are working really bad while others are fairly fine but in the end things will keep getting worse until you have a dead video card.

Likely it is the welds on the card that is bad as you can fix it by putting it in the oven for a couple of minutes, temporarily at least. Fixed 2 8800gts cards and a 6870 this way myself, just make sure you know what you are doing and read up on it before trying! Just search for oven trick and all info should be there.
Also plenty of people who got RMA's trough for the problem, but getting a new card of the same make often did not fix the issue.