After one month of struggling, I think I have finally solved the puzzle. It wasn't the non-working slot on the motherboard as I've previously thought.  The solution is as follows:
I bought a new motherboard. I tested one by one GPU with risers. My first problem was random Win freeze. I found out that 2 of 10 risers have been causing that problem. Namely, with only one card on a new motherboard( with unhealthy riser) it turned out that windows also freezes. I removed those risers and the rig started to work normally.... Except for one additional problem:

Zm miner (dstm) or ewbf miner crash. ( longer time intervals on low clocking settings). I performed the same experiment now, tested one by one GPU, but this time I pushed overclocking almost to the limit. It turned out that I had to throw away two more risers.

To summarise: I noticed that two types of riser problems existed on my rig:
1.  Bad Riser was causing windows to freeze, or restart with blue screen randomly.
2.  Bad Riser was causing Miner to become unstable. ( crashed on longer time intervals).

One interesting thing that I also noticed was that one GPU from 10 that I had( ZOTAC AMP extreme) was unable to run on high overclocking settings( and all other cards were able). I noticed that when I tested the riser on that card. With riser, miner was crashing. I removed the riser, plugged card directly into PCIe 16x slot, and surprisingly the same happened without the riser.( that have never happened with other 9 GPUs) That made me conclude that I have got one card that definitely has worse SMOS integration done. ( Silicon lottery) So I want to emphasize: when you are overclocking your rig, be aware that only one card can limit your max clocking. Test each card separately.

Now I am using Acrefawn's watchdog: https://bitcointalk.org/index.php?topic=2071108.0  It helped me because still, I have some program crashes after few days of running. The batch script automaticly runs a program after a crash. It has also some more advanced features.

I think that I have finally found what was causing the problem. It seems that the last PCIe is not working properly. When I insert extender with the card in it, Win freezes one minute after turning on. Still, have the issue with stability. It works stable only for approximately 15 hours on average. Maybe it's PSU.

I have 10x 1070 on win 1709. The rig is not stable. When I pull out 2 cards, it works pretty much fine. Tried various things. Nothing helps. My screen freezes after some time. That's the major problem.
The system was able to detect 10 GPUs even on the normal win, without fall creators update. (1709)

Thanks for the reply.
Yeah, I think I will end up like people who were trying to find Eldorado. At least, I will get a huge satisfaction by watching my mobo being destroyed to death. After that, I will simply buy two 6 gpus mobos. I think that by trying to solve this problem I have lost money equivalent to at least  6 ordinary mining boards,  if not even more.

Try with NvidiaInspector. The only problem I have is that I can not load saved profiles so I use MSI AB and additional overclocking programme( in my case as I have Zotac cards-Firestorm). WIth msi I oc 8 cards and with Firestorm 2 remaining. But Nvidia Inspector is able to detect >8, so if you are able to load saved profiles that will perfectly work.

Thank you very much for redirecting me to that post. I will try to investigate whether that component causes the problems and I will report.

Have you investigated the temperature dependence on the number of cards? Do you think that specific component that you pictured influences PCIe slots to stop working by transferring heat to them, or you suggest that motherboard has built in feature to stop when some of its elements pass predefined threshold temp. Have you solved the problem with introducing some kind of heating that you mentioned?

The fact that you reported lead either to the conclusion that Asrock ,  ASUS motherboard is not designed properly: it always overheats when there are many gpus (>10) or that you have motherboards that are not working properly or that high power VEGA consumption specifically  heats the board.

In my case I render the picture from the integrated GPU on CPU(i3) but still the picture freezes so I might conclude it's not due to PCIe.

Have you tried to read some motherboard temperatures from HWInfo?

Here is my previous post for other thread so you can know my conf:

''
Hello,
I had the problem that system freezes at random time intervals while mining when using 10 Nvidia cards on H110 motherboard running on windows. I was aware of the limit on windows: 8 nvidia and 5 amd, or other way round so I got an information that windows solved that problem in Fall creators update. Unfortunately, my system was running two days and after that it started to freeze again on random time intervals when mining: approximately 2-3 hours.  I tested both EWBF and DSTM miner. Has anyone reported that this win update can fix the problem?

This is a description my system conf:

Rig:
10x Zotac 1070 AMP Extreme
Asrock H110 Pro BTC
Intel i3
8GB RAM
500 HDD
2x corsair 1000W + Kolink 750W : 2750W

OC:
Power Limit: 65
GPU Core: 70
Memory Core: 270
Target Temp: 70

OS:
Windows 10, Fall creators Update

EWBF: 4600 sol/s   Power usage: 160W/card
DSTM: 4750 sol/s

''

Hello,
I had the problem that system freezes at random time intervals while mining when using 10 Nvidia cards on H110 motherboard running on Win10. I was aware of the limit on Win10: 8 nvidia and 5 amd, or other way round so I got information that windows solved that problem in Fall creators update (1709). Unfortunately, my system was running two days and after that it started to freeze again on random time intervals when mining: approximately 2-3 hours.  I tested both EWBF and DSTM miner. Has anyone reported that this win update can fix the problem?

This is a description my system conf:

Rig:
10x Zotac 1070 AMP Extreme
Asrock H110 Pro BTC
Intel i3
8GB RAM
500 HDD
2x corsair 1000W + Kolink 750W : 2750W

OC:
Power Limit: 65
GPU Core: 70
Memory Core: 270
Target Temp: 70

OS:
Windows 10 1709, Fall creators Update

EWBF: 4600 sol/s   Power usage: 160W/card
DSTM: 4750 sol/s

You are able to run 12 Nvidia cards on windows? Your system is stable?