One expects a few bumps and bruises when using alpha and now beta software and my current project using the eeVee renderer in Blender 2.8 has been haunted by a few problems. Generally though, and a credit to the team producing it, it's been pretty solid.
One problem I have had is renders, and I have some long ones up to 4000 frames, crashing at random places on different computers. Windows does not crash but Blender closes. The Event Viewer says a Blender process had a problem. I have got quite superstitious about it as it never crashes in the same place twice... so it doesn't seem to be anything in the scene content doing it. Also I have had similar problems with very simple blend files... so what's the problem??
One thing I found was that the work is so GPU intensive that my motherboard didn't turn on the chassis fans as the CPU was pretty idle. Making sure the fans are turned up to full when rendering has improved things on the one machine that I can do that on. The others computers have fans that are constantly on.
My rendering computers are ones that once were my main computer but have been superseeded and the same with graphics cards, which get passed down the chain... and powersupplies.
My second computer, which has an i7 and a GTX970 in it, was having some Blender eeVee crashing problems. It had a Silent Pro Gold 550w supply in it so I ordered a second hand 750w Corsair RM supply so see if this was the problem.
I was motivated to get on and switch over the supplies because I had tried to render a 500 frame sequence and it had crashed three times before finishing. Each frame had was taking about 20s mainly due to a lot of depth of field which seems to slow things down.
Now I have swapped over the supplies and it's rendered it in one go... no crashes. 4000 frames.. no problems too :)
It's interesting because I've never really had a problems with Cycles so maybe they use the GPU in a very different way.
SO... It may well be you need a powerful, high quality PSU for eeVeee. I expect the graphics cards deal with slight power problems without complaining but maybe eeVee can't.
If I'd got on and done this when I first suspected it I would have saved myself quite a lot of time.... Even though the 12v rails just meet the spec for the card it might not be good enough for the long render..