Do you get any other channels on the Kordia MUX such as the Freeview|HD Test Channel or Parliament TV? Your issue is probably a signal strength one related to your aerial and I'm picking you don't.
There are no issues recording Prime on Tivo. You just have to manually schedule the recordings since Sky TV refuse to provide their EPG data to Tivo - and Tivo won't use the MHEG5 data that is available on the Freeview platform.
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Try another channel scan. Prime seems to often have up to 5 sec gaps in transmission. You can record Prime but you have to manually set the start and end time. And if you are watching something and hit record it will only record to the next half hour. Everything you record is called "Help us get this EPG contact prime" Quite pathetic really. Makes season pass a joke as prime change the start times of programs all time. Prime advertisers are the big losers, you never know whats on. I miss most the programs I would have liked to watch because there is no program guide. One day either Sky will grow up or Tivo will find another source of the EPG. Until then Tivo-0 Sky-0 Magic TV-1
Do you get Maori TV? I am in Wellington and Maori and Prime are both on frequency 778,000 Mhz here. So if I get sufficient signal strength on one I also get it on the other. Same as for all the other channels which share a frequency such as one and two are both on 690,000 MHZ. As noted above at a guess you have poor signal strength, try adjusting your cabling to remove any loops or kinks, then use the TiVo button on the remote, Settings, Channels, Signal Quality, Select, OK. Although you will likely need to re scan for avaiable channels first. That will show you which channels you have strong signal strength and where its less strong.