Since the last retune, we have an out of group channel at C29. The Humax HDR fails to find or receive it, and I cannot quite make sense of it. It was the weirdest thing - the TV would received it, but only if the Humax was off.
And I just figured out the problem: a cheap HDMI cable from poundland caused interference. With a different HDMI cable, everything is fine. So just in case anybody else has the same problem - check the HDMI cable.