Sorry for the inaccessibility of the site for a few days. In is totally unacceptable, but this is the price for running server at home. The cause of the site outage was good old home router WBR-3406TX. It was really old and it served well till ... the end.

First thing in the yesterday morning I did was to order a new router. I did a little research during the weekend which one to buy. I was totality about
Linksys WRT160NL. It has really some nice features (USB port, detachable antennas) on top of a powerful hardware (400Mhz CPU, for instance). I would flash it with
DD-WRT firmware.
But in the end pragmatism won. I really need only basic routing functionality. So I smartly picked up a
most popular router in one of the popular
Slovene computer hardware store. It is TP-Link TL-WR642G.

Probably you do not know even the manufacture. Do not now worry, I did not either. But anyway, the idea worked perfectly. I got inexpensive reliable router which do exactly what I need and nothing more. And that is what we should always do.
Do nothing more and nothing less what is necessary.