I will keep updating this thread. Maybe it will help someone at some point or I'll get unexpected advise.

So, I tested each and every hash board separately for a couple of hours. All were good without failures.
Then I started adding one more hashboard. Two boards are hashing for around 36 hours at usual hashrate without any failures.

I'll switch Hashboards and keep on checking. If two boards are hashing reliably but not three I suppose it is the PSU? Or just one of it's power cables. I can hardly imagine how the control board might cause such behaviour.