Just trying to check if the homeplugs are faulty. Connect your laptop to the homeplug you use for the humax box and turn off the wireless. If your laptop is still connected to the internet and you can use the laptop to view iplayer they must be working OK. Nothing to do with your TV.
Some homeplugs have power saving, they only turn on when they get network traffic.
Haven't you got a network cable from your Humax box location to your router ? If not can you run one ?