Thank you very much for your response. I have now resolved the problem even though I do not yet know what the exact cause was, but I suspect powerline adapters in my network. Just in case if this turns out to be useful for anyone:
- I traced the problem to TP-link powerline adapters within my LAN - rebooting them immediately (but temporarily) solved the symptoms until the problem resurfaced hours later. Rebooting them again helped again.
- I tried isolating those powerline adapters within a different subnet, but it did not help as long as that subnet touched the RUTX10 device in question.
- I moved those powerline adapters under a different RUTX10 device that was running a newer firmware version (RUTX_R_00.07.08) that was isolating the RUTX10 device in the question; this way powerline adapters ended up on a subnet that did not even touch the original RUTX10 device.
- When I saw that the other RUTX10 device was working fine, I also updated firmware of my main router from RUTX_R_00.07.07 to 08.
While I appreciate the the above description did not exactly troubleshoot the problem, I had no time to do all A/B experiments. i stopped tinkering when my home network became stable enough foe me to work. I do not fully understand how powerline adapters work and what kind of virtual switching interface they implement. I was using 3 of them in my network and in theory I was not supposed to have a switching loop, as two of them were connected to clients and one of them was connected to the RUTX10, but who knows.