Firstly, disconnect the HDMI cable and see if it still does it. If so, look for CEC on the TV and turn it off. CEC is one name for control of the TV from the HDMI input. It is called other names depending on the make of TV.
Also worth checking would be to see if the TV has some sort of auto off that switches it off after (say) two hours of no remote control input.
When you say ‘switches off to a blank screen’, do you mean it really switches right off or you just lose the picture and/or sound?
Another fix might be instead of feeding the TV via the Humax, use a passive two way splitter instead. In fact just thought that this might be the problem if the Humax goes into deep sleep mode and switches off the aerial feed through. To prevent this switch off the power saving standby mode.