Hello Guys,
Sorry for the late answer.
I have replaced the resistors on my modules.
For trial I replaced all resistors on first module to 43Ohm, on the other to 39Ohm.
The situation is a bit better, I have 'only' few non-functional relays.
I opened the enlosure lid, knocking with screwdriwer on the top of the relys, it is working now again for a while.
Those relays what I user every day few times, there is no any issue with them. The relay what are used only once a week can stuck in again...

I am thinking on to replace all the Omron relays to an other brand, but it is not a cheap investment for blind guess.
Yeah, the 12V power supply is fine, there is no issue with that. I have two modules, statistically must be good.
I'm going to try to translate the Polish answers
