Somehow better: Varnish caches were oversized on our current amount of RAM and slowly saturated all resources, some previous connection failed (Guru Meditation = web server unable to provide fresh contents to first-line cache) and tonight (CET timezone) I found the server completely unable to serve new requests due memory saturation.
Now I've limited size of those buffers and situation reached a new balance, it needs more tuning but at least services are available again after the latest crisis.
Thanks to Nick Gammon to alert me by mail about the recent issue.